Global set theory seminar and conference announcements
Talk by Andrés Villaveces tomorrow (1 30 pm)
Toronto Set Theory Seminar
2/4/2021 14:30:00
Hello everyone,
Please use the following link and fill the form (every week) to
enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
Speaker :Andrés Villaveces, Universidad Nacional de Colombia
Date and Time: Friday, February 5, 2021 - 1:30pm to 3:00pm
Title: Axiomatizations of abstract elementary classes and natural logics for model theory: the role of partition relations.
Abstract:
Two
seemingly unrelated questions (the quest for natural logics of abstract
elementary classes on the one hand, and the quest for logics adequate
to model theory on the other hand) converge around the same
combinatorial core: partition relations for scattered order types (due
to Kómjath and Shelah). I will present recent results concerning the
first question (and axiomatizing a.e.c.'s - joint work with Shelah) and
the second question (joint work with Väänänen).
Bio: Andrés Villaveces is a mathematician, working at Universidad
Nacional de Colombia in Bogotá. Villaveces earned his doctoral degree
from the University of Wisconsin-Madison in 1996 under the supervision
of Ken Kunen. He held a postdoctoral position at the Hebrew University
of Jerusalem (1996-1997) and has been a visiting professor at Carnegie
Mellon University (2002-2003) and at the University of Helsinki (2007
and 2015). His work centers on the model theory of Abstract Elementary
Classes and its connections with set theory and other parts of logic and
mathematics.
Please use the following link and fill the form (every week) to
enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
Speaker :Andrés Villaveces, Universidad Nacional de Colombia
Date and Time: Friday, February 5, 2021 - 1:30pm to 3:00pm
Title: Axiomatizations of abstract elementary classes and natural logics for model theory: the role of partition relations.
Abstract:
Two
seemingly unrelated questions (the quest for natural logics of abstract
elementary classes on the one hand, and the quest for logics adequate
to model theory on the other hand) converge around the same
combinatorial core: partition relations for scattered order types (due
to Kómjath and Shelah). I will present recent results concerning the
first question (and axiomatizing a.e.c.'s - joint work with Shelah) and
the second question (joint work with Väänänen).
Bio: Andrés Villaveces is a mathematician, working at Universidad
Nacional de Colombia in Bogotá. Villaveces earned his doctoral degree
from the University of Wisconsin-Madison in 1996 under the supervision
of Ken Kunen. He held a postdoctoral position at the Hebrew University
of Jerusalem (1996-1997) and has been a visiting professor at Carnegie
Mellon University (2002-2003) and at the University of Helsinki (2007
and 2015). His work centers on the model theory of Abstract Elementary
Classes and its connections with set theory and other parts of logic and
mathematics.
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
James Walsh, Cornell University Reducing omega-model reflection to iterated syntactic reflection
Two types of principles are commonly called “reflection principles” in reverse mathematics. According to syntactic reflection principles for T, every theorem of T (from some complexity class) is true. According to semantic reflection principles, every set belongs to some (sufficiently correct) model of T. We will present a connection between syntactic reflection and semantic reflection in second-order arithmetic: for any Pi^1_2 axiomatized theory T, every set is contained in an omega model of T if and only if every iteration of Pi^1_1 reflection for T along a well-ordering is Pi^1_1 sound. There is a thorough proof-theoretic understanding of the latter in terms of ordinal analysis. Accordingly, these reductions yield proof-theoretic analyses of omega-model reflection principles. This is joint work with Fedor Pakhomov.
- - - - Wednesday, Feb 3, 2021 - - - -
The New York City Category Theory Seminar
Speaker: Jason Parker, Brandon University in Manitoba.
Date and Time: Wednesday February 3, 2021, 7:00 - 8:30 PM., on Zoom.
Title: Isotropy Groups of Quasi-Equational Theories.
Abstract: In [2], my PhD supervisors (Pieter Hofstra and Philip Scott) and I studied the new topos-theoretic phenomenon of isotropy (as introduced in [1]) in the context of single-sorted algebraic theories, and we gave a logical/syntactic characterization of the isotropy group of any such theory, thereby showing that it encodes a notion of inner automorphism or conjugation for the theory. In the present talk, I will summarize the results of my recent PhD thesis, in which I build on this earlier work by studying the isotropy groups of (multi-sorted) quasi-equational theories (also known as essentially algebraic, cartesian, or finite limit theories). In particular, I will show how to give a logical/syntactic characterization of the isotropy group of any such theory, and that it encodes a notion of inner automorphism or conjugation for the theory. I will also describe how I have used this characterization to exactly characterize the ‘inner automorphisms’ for several different examples of quasi-equational theories, most notably the theory of strict monoidal categories and the theory of presheaves valued in a category of models. In particular, the latter example provides a characterization of the (covariant) isotropy group of a category of set-valued presheaves, which had been an open question in the theory of categorical isotropy.
[1] J. Funk, P. Hofstra, B. Steinberg. Isotropy and crossed toposes. Theory and Applications of Categories 26, 660-709, 2012.
[2] P. Hofstra, J. Parker, P.J. Scott. Isotropy of algebraic theories. Electronic Notes in Theoretical Computer Science 341, 201-217, 2018.
- - - - Thursday, Feb 4, 2021 - - - -
- - - - Friday, Feb 5, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Feb 5, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Andreas Blass, University of Michigan Choice from Finite Sets: A Topos View
Tarski proved (but didn't publish) the theorem that choice from pairs implies choice from four-element sets. Mostowski (1937) began a systematic study of such implications between choice axioms for families of finite sets. Gauntt (1970) completed that study (but didn't publish the results), obtaining equivalent characterizations in terms of fixed points of permutation groups. Truss (1973) extended Gauntt's results (and published this work).
It turns out that these finite choice axioms and their group-theoretic characterizations are instances of the same topos-theoretic statements, interpreted in two very different classes of topoi. My main result is an extension of that observation to the class of all topoi.
Most of my talk will be explaining the background: finite choice axioms, permutation groups, and a little bit about topoi - just enough to make sense of the main result. If time permits, I'll describe some of the ingredients of the proof.
Next Week in Logic at CUNY:
- - - - Monday, Feb 8, 2021 - - - -
Logic and Metaphysics Workshop Date: Monday, Feb 8, 4.15-6.15 (NY time) For meeting information, please email: yweiss@gradcenter.cuny.edu Patrick Girard, Auckland
- - - - Tuesday, Feb 9, 2021 - - - -
Models of Peano Arithmetic (MOPA)
Wednesday, Feb 9, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
An isomorphism theorem for models of Weak Kőnig's Lemma without induction
We prove that any two countable models of the theory WKL∗0WKL0∗ sharing the same first-order universe and containing the same counterexample to Σ01Σ10 induction are isomorphic.
This theorem implies that over WKL∗0+¬IΣ01WKL0∗+¬IΣ10, the analytic hierarchy collapses to the arithmetic hierarchy. It also implies that WKL∗0WKL0∗ is the strongest Π12Π21 statement that is Π11Π11-conservative over RCA∗0+¬IΣ01RCA0∗+¬IΣ10. Together with the (slightly subtle) generalizations of the theorem to higher levels of the arithmetic hierarchy, this gives an 'almost negative' answer to a question of Towsner, who asked whether Π11Π11-conservativity of Π12Π21 sentences over collection principles is a Π02Π20-complete computational problem. Our results also have some implications for the reverse mathematics of combinatorial principles: for instance, we get a specific Π11Π11 sentence that is provable in RCA0+BΣ02RCA0+BΣ20 exactly if the Π11Π11 consequences of RCA0+RT22RCA0+RT22 coincide with BΣ02BΣ20.
On the side, we also give a positive answer to Towsner's question as originally stated.
Joint work with Marta Fiori Carones, Tin Lok Wong, and Keita Yokoyama.
- - - - Wednesday, Feb 10, 2021 - - - -
The New York City Category Theory Seminar
Speaker: Peter Hines University of York.
Date and Time: Wednesday February 10, 2021, 7:00 - 8:30 PM., on Zoom.
Title: Invertibility in Operads : an elementary arithmetic approach.
Abstract: This talk is motivated by two areas of 'lost mathematics' -- topics where it is clear that interesting theory was once known & understood, but only incomplete traces remain in the historical record. One of these was due to ancient Greek mathematicians & logicians, and the other is a much lesser-known relation of a famous open problem from the 20th century.
One objective of this talk is to trace a link between the two. However, this is not an exercise in the 'History of Mathematics' -- the connections rely on theory that certainly was not understood in either time period.
Precisely, we consider 'Invertible Operads' -- that is, those whose composition operations are either partially or globally invertible. We look at examples that are freely generated by some given set of operations, with particular reference to those whose composition operations may be given by elementary arithmetic functions.
We demonstrate how such structures arise in a range of different topics, providing previously unobserved connections between them. This includes subjects such as standard Young tableaux, mixed-radix counting systems, topologies on the natural numbers, logical models, famous groups, and combinatorially-inspired polyhedra.
This is very much work in progress, and aims to present interesting questions as much as interesting structures and results.
- - - - Thursday, Feb 11, 2021 - - - -
- - - - Friday, Feb 12, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Feb 12, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Bea Adam-Day, University of Leeds
- - - - Other Logic News - - - -
- - - - Web Site - - - -
"Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)"
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Barcelona Set theory Seminar
Barcelona Logic Seminar
1/31/2021 17:02:10
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Adrian Mathias (Université de la Réunion)
TITLE: Power-admissible sets and ill-founded omega-models of weak subsystems of ZFC
TIME: February 3 at 16:00 (CET)
PLACE: The Seminar will take place online at the following address:
TUESDAY, February 2, 2021
Mathematical logic seminar: 3:30 P.M., Online, Anush Tserunyan, McGill
University
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Ergodic theorems along trees
ABSTRACT: In the classical pointwise ergodic theorem for a probability
measure preserving (pmp) transformation $T$, one takes averages of a given
integrable function over the intervals $\{x, T(x), T^2(x), \hdots,
T^n(x)\}$ in front of the point $x$. We prove a “backward” ergodic theorem
for a countable-to-one pmp $T$, where the averages are taken over subtrees
of the graph of T that are rooted at $x$ and lie behind $x$ (in the
direction of $T^{-1}$). Surprisingly, this theorem yields forward ergodic
theorems for countable groups, in particular, one for pmp actions of free
groups of finite rank, where the averages are taken along subtrees of the
standard Cayley graph rooted at the identity. This strengthens Bufetov’s
theorem from 2000, which was the most general result in this vein. This is
joint work with Jenna Zomback.
TUESDAY, February 2, 2021
Set Theory Reading Group: 4:30 P.M., Online, Jenna Zomback, University of
Illinois at Urbana-Champaign
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Ergodic theorems along trees: the proofs
ABSTRACT: In this continuation of the previous talk, we discuss a backward
(inverse) ergodic theorem for a probability measure preserving (pmp)
transformation $T$, where the averages are taken over subtrees of the
graph of $T$ that are rooted at $x$ and lie behind $x$ (in the direction
of $T^{-1}$). We will derive from it a new (forward) pointwise ergodic
theorem for pmp actions of free groups of finite rank, where the averages
are taken along subtrees of the standard Cayley graph rooted at the
identity. We will then discuss a very short proof (due to Tserunyan) of
the classical pointwise ergodic theorem, and, using this proof as an
outline, we will sketch the proof of the backward ergodic theorem. This is
joint work with Anush Tserunyan.
THURSDAY, February 4, 2021
Model Theory Seminar: 10:00 A.M., Online, John Baldwin, UIC
Join Zoom Meeting:
https://cmu.zoom.us/j/96301869290?pwd=Qk1zS0h6ZThmUnRpbmNLNkVJSjkrQT09
Meeting ID: 963 0186 9290
Passcode: 567655
TITLE: The Hanf number for extendability is the first measurable cardinal,
Part 1
ABSTRACT: We prove in ZFC the existence of a complete sentence of
infinitary logic that has maximal models in a set of cardinals cofinal in
the first measurable but no maximal models in any cardinal beyond the
first measurable. As a warmup to the first lecture please look at the
Motivation http://homepages.math.uic.edu/~jbaldwin/pub/cmupre
This is joint work with Saharon Shelah.
Preprints are available at
http://homepages.math.uic.edu/~jbaldwin/pub/ahanfmaxjan21.pdf and
http://homepages.math.uic.edu/~jbaldwin/pub/ahazfjan7.pdf
TUESDAY, February 9, 2021
Mathematical logic seminar: 3:30 P.M., Online, Benjamin Siskind,
University of California, Berkeley
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Order-preserving Martin’s Conjecture
ABSTRACT: Martin’s Conjecture is a precise way of asserting that, up to
equivalence, the only natural functions on the Turing degrees are the
familiar ones: the constant functions, the identity, the Turing jump, and
the transfinite iterates of the Turing jump. This conjecture is open even
restricted to low-level Borel functions, but there have been partial
results over the years which show it holds for classes of functions
meeting requirements orthogonal to definability. Our recent result is that
part of Martin’s Conjecture (lately called “part one”) holds for the class
of order-preserving functions. In particular, it follows that the full
Martin’s Conjecture holds for Borel order-preserving functions. We’ll talk
about Martin’s Conjecture broadly and say something about this recent
work. This is joint work with Patrick Lutz.
TUESDAY, February 9, 2021
Set Theory Reading Group: 4:30 P.M., Online, Benjamin Siskind, University
of California, Berkeley
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Measure-preserving functions on the Turing degrees
ABSTRACT: One proof of part one of Martin’s Conjecture for
order-preserving functions works for a bigger class of functions: those
which are measure-preserving for the Martin measure, in the sense of
ergodic theory. Looking at this class of functions brings out more
set-theoretic aspects of Martin’s Conjecture. For example, part one of
Martin’s Conjecture is equivalent to the non-existence of other
non-principal ultrafilters on the Turing degrees Rudin-Keisler below the
Martin measure. We’ll talk about the proof of part one of Martin’s
Conjecture for this class of functions and some consequences. This is
joint work with Patrick Lutz.
THURSDAY, February 11, 2021
Model Theory Seminar: 10:00 A.M., Online, John Baldwin, UIC
Join Zoom Meeting:
https://cmu.zoom.us/j/96301869290?pwd=Qk1zS0h6ZThmUnRpbmNLNkVJSjkrQT09
Meeting ID: 963 0186 9290
Passcode: 567655
TITLE: The Hanf number for extendability is the first measurable cardinal,
Part 2
ABSTRACT: We prove in ZFC the existence of a complete sentence of
infinitary logic that has maximal models in a set of cardinals cofinal in
the first measurable but no maximal models in any cardinal beyond the
first measurable. As a warmup to the first lecture please look at the
Motivation http://homepages.math.uic.edu/~jbaldwin/pub/cmupre
This is joint work with Saharon Shelah.
Preprints are available at
http://homepages.math.uic.edu/~jbaldwin/pub/ahanfmaxjan21.pdf and
http://homepages.math.uic.edu/~jbaldwin/pub/ahazfjan7.pdf
TUESDAY, February 16, 2021
Mathematical logic seminar: 3:30 P.M., Online, Aristotelis
Panagiotopoulos, University of Muenster
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: The definable content of (co)homological invariants: Cech
cohomology
ABSTRACT: In this talk we will develop a framework for enriching various
classical invariants of homological algebra and algebraic topology with
additional descriptive set-theoretic information. The resulting "definable
invariants" can be used for much finer classification than their purely
algebraic counterparts. We will then illustrate how these ideas apply to
the classical Cech cohomology theory, by introducing a new invariant for
locally compact metrizable spaces up to homotopy equivalence which we call
"definable cohomology". In strong contrast to its classical counterpart,
this definable cohomology theory provides complete classification to
homotopy classes of mapping telescopes of d-tori, and for homotopy classes
of maps from mapping telescopes of d-tori to spheres. The latter problem
was raised in the d=1 case by Borsuk and Eilenberg in 1936.
This is joint work with Jeffrey Bergfalk and Martino Lupini.
TUESDAY, February 16, 2021
Set Theory Reading Group: 4:30 P.M., Online, Aristotelis Panagiotopoulos,
University of Muenster
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Ulam stability for quotients of abelian non-archimedean Polish
groups
ABSTRACT: Based on an earlier work of Shelah concerning the relationship
of the continuum hypothesis to the cardinality of the set of automorphisms
of $\mathcal{P}(\omega)/\mathrm{fin}$, Velickovic showed that if such an
automorphism admits a Borel lift $\mathcal{P}(\omega)\to
\mathcal{P}(\omega)$, then it is of a certain "trivial" form. Similarly,
Kanovei and Reeken showed that if $N,M$ are countable dense subgroups of
$\mathbb{R}$, then every homomorphism $\mathbb{R}/N\to \mathbb{R}/M$ with
a Borel lift $\mathbb{R}\to \mathbb{R}$, is of a certain "trivial" form.
Kanovei and Reeken asked whether quotients of the $p$-adic groups satisfy
similar "Ulam stability" phenomena. In this talk, we will settle this
question by providing Ulam-stability phenomena for definable homomorphisms
$G/N\to H/M$ when $G,H$ are arbitrary abelian non-archimedean Polish
groups and $N,M$ are Polishable subgroups. We will then illustrate how
such rigidity results are in the heart of the definable cohomology theory
which we developed in the previous talk.
This is joint work with Jeffrey Bergfalk and Martino Lupini.
TUESDAY, March 2, 2021
Mathematical logic seminar: 3:30 P.M., Online, Marc Noy, Technical
University of Catalonia
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Zero-One and Convergence Laws for Graphs Embeddable on a Fixed
Surface
ABSTRACT: Let G be a class of labeled graphs with the uniform probability
distribution on graphs with a fixed number of vertices. Given a graph
property A, we are interested in the limiting probability that A holds in
G. It was shown by Heinig et al. that this limiting probability always
exists when G is the class of planar graphs and A is any property
expressible in monadic second order logic (MSO), and it was conjectured
that the same result holds for the class of graphs embeddable on a fixed
surface S. After reviewing the results for planar graphs, and more
generally for minor-closed classes of graphs, we will refute the
conjecture by showing that for every closed surface (orientable or not)
other than the sphere there exists an MSO graph property whose limiting
probability does not exist. In addition we show that every rational number
in [0,1] is the limiting probability of some MSO property, as opposed to
the class of planar graphs where there are so-called gaps. The proof
relies on a combination of methods from structural graph theory,
concretely large face-width embeddings of graphs on surfaces, analytic
combinatorics, and finite model theory.
This is joint work with Albert Atserias and Stephan Kreutzer.
TUESDAY, April 20, 2021
Mathematical logic seminar: 3:30 P.M., Online, Sandra Müller, University
of Vienna
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: TBA
TUESDAY, April 20, 2021
Set Theory Reading Group: 4:30 P.M., Online, Sandra Müller, University of
Vienna
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: TBA
Tomorrow: Corey Switzer at 1 30 pm (Toronto Time)
Toronto Set Theory Seminar
1/28/2021 13:01:00
Hello everyone,
Please use the following link and fill the form (every week) to
enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
Date and Time: Friday, January 29, 2021 - 1:30pm to 3:00pm (Toronto time)
Title: Higher Dimensional Cardinal Characteristics for Sets of Real Valued Functions
Abstract:
Cardinal characteristics on the generalized Baire
and Cantor spaces $\kappa^\kappa$ and $2^\kappa$ have recently generated
significant interest. In this talk I will introduce a different
generalization of cardinal characteristics, namely
to the space of functions $f:\omega^\omega \to \omega^\omega$. Given an
ideal $I$ on Baire space and a relation $R$ let us define $f R_I g$ for
$f$ and $g$ functions from $\omega^\omega$ to $\omega^\omega$ if and
only if $f(x) R g(x)$ for an $I$-measure one
set of $x \in \omega^\omega$. By letting $I$ vary over the null ideal,
the meager ideal and the bounded ideal; and $R$ vary over the relations
$\leq^*$, $\neq^*$ and
$\in^*$
we get 18 new cardinal characteristics by considering the bounding and
dominating numbers for these relations. These new cardinals form a
diagram of provable implications similar to the Cichoń diagram.
They also interact in several surprising ways with the cardinal
characteristics on $\omega$. For instance, they can be arbitrarily large
in models of CH, yet they can be
$\aleph_1$
in models where the continuum is arbitrarily large. They are bigger in
the Sacks model than the Cohen model. I will introduce these cardinals,
show some of the provable implications and discuss
what is known about consistent inequalities, focusing on the
$\mathfrak{b}$-numbers in well-known models such as the Cohen and Random
model. This is joint work with Jörg Brendle.
Bio: Corey Bacal Switzer is currently a postdoctoral researcher at
the Kurt Gödel Research Center For Mathematical Logic in the Mathematics
Department of the University of Vienna working under Vera Fischer. He
finished his PhD at the CUNY Graduate Center in New York in 2020. His
research is in set theory, focusing on forcing, cardinal characteristics
and infinite combinatorics
Logic Seminar 3 Feb 2021 17:00 hrs at NUS by Wong Tin Lok
NUS Logic Seminar
1/28/2021 3:41:46
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 3 February 2021, 17:00 hrs
Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Speaker: Wong Tin Lok
Title: Arithmetic under negated induction
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
Arithmetic generally does not admit any non-trivial quantifier
elimination. I will talk about one exception, where the negation of
an induction axiom is included in the theory. Here the Weak Koenig's
Lemma from reverse mathematics arises as a model completion.
This work is joint with Marta Fiori-Carones, Leszek Aleksander Kolodziejczyk
and Keita Yokoyama.
Barcelona Set theory Seminar
Barcelona Logic Seminar
1/25/2021 11:50:42
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Richard Matthews (Univ. of Leeds)
TITLE: Taking Reinhardt’s Power Away
TIME: January 27 at 16:00 (CET)
PLACE: The Seminar will take place online at the following address:
(KGRC) research seminar talk on Thursday, January 28
Kurt Godel Research Center
1/25/2021 11:33:35
Research seminar
Kurt Gödel Research Center
Thursday, January 28
"Distributivity spectrum of forcing notions"
Marlene Koelbing (KGRC), Wolfgang Wohofsky (KGRC)
In our talk, we will introduce two different notions of a spectrum of
distributivity of forcings.
The first one is the fresh function spectrum, which is the set of regular
cardinals lambda, such that the forcing adds a new function with domain lambda
all whose initial segments are in the ground model. We will provide several
examples as well as general facts how to compute the fresh function spectrum,
also discussing what sets are realizable as a fresh function spectrum of a
forcing.
The second notion is the combinatorial distributivity spectrum, which is the
set of possible regular heights of refining systems of maximal antichains
without common refinement. We discuss the relation between the fresh function
spectrum and the combinatorial distributivity spectrum. We consider the special
case of P(omega)/fin (for which h is the minimum of the spectrum), and use a
forcing construction to show that it is consistent that the combinatorial
distributivity spectrum of P(omega)/fin contains more than one element.
This is joint work with Vera Fischer.
Time and Place
Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not
received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
This Friday Talk: Corey Switzer (usual time)
Toronto Set Theory Seminar
1/25/2021 9:03:43
Hello everyone,
Please use the following link and fill the form (every week) to
enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
Date and Time: Friday, January 29, 2021 - 1:30pm to 3:00pm
Title: Higher Dimensional Cardinal Characteristics for Sets of Real Valued Functions
Abstract:
Cardinal characteristics on the generalized Baire
and Cantor spaces $\kappa^\kappa$ and $2^\kappa$ have recently generated
significant interest. In this talk I will introduce a different
generalization of cardinal characteristics, namely
to the space of functions $f:\omega^\omega \to \omega^\omega$. Given an
ideal $I$ on Baire space and a relation $R$ let us define $f R_I g$ for
$f$ and $g$ functions from $\omega^\omega$ to $\omega^\omega$ if and
only if $f(x) R g(x)$ for an $I$-measure one
set of $x \in \omega^\omega$. By letting $I$ vary over the null ideal,
the meager ideal and the bounded ideal; and $R$ vary over the relations
$\leq^*$, $\neq^*$ and
$\in^*$
we get 18 new cardinal characteristics by considering the bounding and
dominating numbers for these relations. These new cardinals form a
diagram of provable implications similar to the Cichoń diagram.
They also interact in several surprising ways with the cardinal
characteristics on $\omega$. For instance, they can be arbitrarily large
in models of CH, yet they can be
$\aleph_1$
in models where the continuum is arbitrarily large. They are bigger in
the Sacks model than the Cohen model. I will introduce these cardinals,
show some of the provable implications and discuss
what is known about consistent inequalities, focusing on the
$\mathfrak{b}$-numbers in well-known models such as the Cohen and Random
model. This is joint work with Jörg Brendle.
Bio: Corey Bacal Switzer is currently a postdoctoral researcher at
the Kurt Gödel Research Center For Mathematical Logic in the Mathematics
Department of the University of Vienna working under Vera Fischer. He
finished his PhD at the CUNY Graduate Center in New York in 2020. His
research is in set theory, focusing on forcing, cardinal characteristics
and infinite combinatorics
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Erin Carmody, Fordham University The relationships between measurable and strongly compact cardinals: Part II
This talk is about the ongoing investigation of the relationships between measurable and strongly compact cardinals. I will present some of the history of the theorems in this theme, including Magidor's identity crisis, and give new results. The theorems presented are in particular about the relationships between strongly compact cardinals and measurable cardinals of different Mitchell orders. One of the main theorems is that there is a universe where κ1κ1 and κ2κ2 are the first and second strongly compact cardinals, respectively, and where κ1κ1 is least with Mitchell order 1, and κ2κ2 is the least with Mitchell order 2. Another main theorem is that there is a universe where κ1κ1 and κ2κ2 are the first and second strongly compact cardinals, respectively, with κ1κ1 the least measurable cardinal such that o(κ1)=2o(κ1)=2 and κ2κ2 the least measurable cardinal above κ1κ1. This is a joint work in progress with Victoria Gitman and Arthur Apter.
Next Week in Logic at CUNY:
- - - - Monday, Feb 1, 2021 - - - -
- - - - Tuesday, Feb 2, 2021 - - - -
Models of Peano Arithmetic (MOPA)
Wednesday, Dec 9, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
James Walsh, Cornell University Reducing omega-model reflection to iterated syntactic reflection
Two types of principles are commonly called “reflection principles” in reverse mathematics. According to syntactic reflection principles for T, every theorem of T (from some complexity class) is true. According to semantic reflection principles, every set belongs to some (sufficiently correct) model of T. We will present a connection between syntactic reflection and semantic reflection in second-order arithmetic: for any Pi^1_2 axiomatized theory T, every set is contained in an omega model of T if and only if every iteration of Pi^1_1 reflection for T along a well-ordering is Pi^1_1 sound. There is a thorough proof-theoretic understanding of the latter in terms of ordinal analysis. Accordingly, these reductions yield proof-theoretic analyses of omega-model reflection principles. This is joint work with Fedor Pakhomov.
- - - - Wednesday, Feb 3, 2021 - - - -
- - - - Thursday, Feb 4, 2021 - - - -
- - - - Friday, Feb 5, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Feb 5, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Andreas Blass, University of Michigan
TBA
- - - - Other Logic News - - - -
- - - - Web Site - - - -
"Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)"
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Two talks by B. Siskind on February 9
Carnegie Mellon Logic Seminar
1/22/2021 21:22:24
TUESDAY, February 9, 2021
Mathematical logic seminar: 3:30 P.M., Online, Benjamin Siskind,
University of California, Berkeley
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Order-preserving Martin’s Conjecture
ABSTRACT: Martin’s Conjecture is a precise way of asserting that, up to
equivalence, the only natural functions on the Turing degrees are the
familiar ones: the constant functions, the identity, the Turing jump, and
the transfinite iterates of the Turing jump. This conjecture is open even
restricted to low-level Borel functions, but there have been partial
results over the years which show it holds for classes of functions
meeting requirements orthogonal to definability. Our recent result is that
part of Martin’s Conjecture (lately called “part one”) holds for the class
of order-preserving functions. In particular, it follows that the full
Martin’s Conjecture holds for Borel order-preserving functions. We’ll talk
about Martin’s Conjecture broadly and say something about this recent
work. This is joint work with Patrick Lutz.
TUESDAY, February 9, 2021
Set Theory Reading Group: 4:30 P.M., Online, Benjamin Siskind, University
of California, Berkeley
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Measure-preserving functions on the Turing degrees
ABSTRACT: One proof of part one of Martin’s Conjecture for
order-preserving functions works for a bigger class of functions: those
which are measure-preserving for the Martin measure, in the sense of
ergodic theory. Looking at this class of functions brings out more
set-theoretic aspects of Martin’s Conjecture. For example, part one of
Martin’s Conjecture is equivalent to the non-existence of other
non-principal ultrafilters on the Turing degrees Rudin-Keisler below the
Martin measure. We’ll talk about the proof of part one of Martin’s
Conjecture for this class of functions and some consequences. This is
joint work with Patrick Lutz.
Tomorrow two talks (11 am and 1 30 pm)
Toronto Set Theory Seminar
1/21/2021 12:00:00
Hello everyone,
To start the semester we will have two talks: one at 11 am (Toronto time) and another at 1 30 pm (Toronto time).
Please use the following link and fill the form (every week) to
enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
Speaker:Dima Sinapova, UIC, University of Illinois at Chicago, University of Illinois, Chicago
Date and Time: Friday, January 22, 2021 - 11am to 12:30pm
Title: Iteration, reflection, and singular cardinals
Abstract:
Two classical results of Magidor are: (1) from large cardinals it is consistent to have reflection at
$\aleph_{\omega+1}$ and (2) from large cardinals it is consistent to have the failure of SCH at $\aleph_{\omega}$.
These principles are at odds with each other. The former is a
compactness type principle. (Compactness is the phenomenon where if a
certain property holds for every smaller substructure of an object, then
it holds for the entire object.) In contrast, failure of SCH is an
instance of incompactness. The natural question is whether we can have
both of these simultaneously. We show the answer is yes.
We describe a Prikry style iteration, and use it to force stationary
reflection in the presence of not SCH. Then we obtain this situation at
$\aleph_{\omega}$
. This is joint work with Alejandro Poveda and Assaf Rinot.
Speaker: Marcos Mazari Armida, Carnagie Mellon University
Date and Time: Friday, January 22, 2021 - 1:30pm to 3pm
Title: Universal models in classes of abelian groups and modules
Abstract:
The search for universal models began in the early twentieth century
when Hausdorff showed that there is a universal linear order of
cardinality $\aleph_{n+1}$ if $2^{\aleph_n}= \aleph_{n + 1}$, i.e., a
linear order $U$ of cardinality $\aleph_{n+1}$ such that every linear
order of cardinality $\aleph_{n+1}$ embeds in $U$. In this talk, we will
study universal models in several classes of abelian groups and modules
with respect to pure embeddings. In particular, we will present a
complete solution below $\aleph_\omega$, with the exception of
$\aleph_0$ and $\aleph_1$, to Problem 5.1 in page 181 of \emph{Abelian
Groups} by L\'{a}szl\'{o} Fuchs, which asks to find the cardinals
$\lambda$ such that there is a universal abelian p-group for purity of
cardinality $\lambda$. The solution presented will use both
model-theoretic and set-theoretic ideas.
TUESDAY, February 16, 2021
Mathematical logic seminar: 3:30 P.M., Online,
Aristotelis Panagiotopoulos, University of Muenster
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: The definable content of (co)homological invariants: Cech cohomology
ABSTRACT: In this talk we will develop a framework for enriching various
classical invariants of homological algebra and algebraic topology with
additional descriptive set-theoretic information. The resulting "definable
invariants" can be used for much finer classification than their purely
algebraic counterparts. We will then illustrate how these ideas apply to the
classical Cech cohomology theory, by introducing a new invariant for locally
compact metrizable spaces up to homotopy equivalence which we call "definable
cohomology". In strong contrast to its classical counterpart, this definable
cohomology theory provides complete classification to homotopy classes of
mapping telescopes of d-tori, and for homotopy classes of maps from mapping
telescopes of d-tori to spheres. The latter problem was raised in the d=1 case
by Borsuk and Eilenberg in 1936.
This is joint work with Jeffrey Bergfalk and Martino Lupini.
TUESDAY, February 16, 2021
Set Theory Reading Group: 4:30 P.M., Online, Aristotelis Panagiotopoulos,
University of Muenster
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Ulam stability for quotients of abelian non-archimedean Polish groups
ABSTRACT: Based on an earlier work of Shelah concerning the relationship of the
continuum hypothesis to the cardinality of the set of automorphisms of
$\mathcal{P}(\omega)/\mathrm{fin}$, Velickovic showed that if such an
automorphism admits a Borel lift $\mathcal{P}(\omega)\to \mathcal{P}(\omega)$,
then it is of a certain "trivial" form. Similarly, Kanovei and Reeken showed
that if $N,M$ are countable dense subgroups of $\mathbb{R}$, then every
homomorphism $\mathbb{R}/N\to \mathbb{R}/M$ with a Borel lift $\mathbb{R}\to
\mathbb{R}$, is of a certain "trivial" form. Kanovei and Reeken asked whether
quotients of the $p$-adic groups satisfy similar "Ulam stability" phenomena. In
this talk, we will settle this question by providing Ulam-stability phenomena
for definable homomorphisms $G/N\to H/M$ when $G,H$ are arbitrary abelian
non-archimedean Polish groups and $N,M$ are Polishable subgroups. We will then
illustrate how such rigidity results are in the heart of the definable
cohomology theory which we developed in the previous talk.
This is joint work with Jeffrey Bergfalk and Martino Lupini.
On Logic Seminar This Semester
NUS Logic Seminar
1/19/2021 2:58:41
Dear Attendees of the logic seminar,
I would like to ask for volunteers who can give talks over Zoom at
17:00 hrs Singapore time, see
http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
for free time-slots (currently all and I will put the names of those
who reserve a slot into their preferred time-slot). Furthermore, for
tomorrow, you might consider attending the talk of Brian Rabern from
the University of Edinburgh at FASS on quantification as modelled by
Frege and by Taski and the philosophical discussion will be moderated
by Ben Blumson, NUS.
Best regards, Frank
`
(KGRC) research seminar talk on Thursday, January 21
Kurt Godel Research Center
1/18/2021 16:20:59
Research seminar
Kurt Gödel Research Center
Thursday, January 21
"Strong colourings over partitions"
Juris Steprāns
(York University, Toronto, Canada)
The celebrated result of Todorcevic that $\aleph_1\not\rightarrow
[\aleph_1]^2_{\aleph_1}$ provides a well known example of a strong colouring. A
mapping $c:[\omega_1]^2\to \kappa$ is a strong colouring over a partition
$p:[\omega_1]^2\to \omega$ if for every uncountable $X\subseteq \omega_1$ there
is $n\in \omega$ such that the range of $c$ on $[X]^2\cap p^{-1}\{n\}$ is all
of $\kappa$. I will discuss some recent work with A. Rinot and M. Kojman on
negative results concerning strong colourings over partitions and their
relation to classical results in this area.
Time and Place
Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not
received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
Barcelona Set theory Seminar
Barcelona Logic Seminar
1/17/2021 15:37:58
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Vera Fisher (Wien)
TITLE: Independent families in the countable and the uncountable
TIME: January 20 at 16:00 (CET)
PLACE: The Seminar will take place online at the following address:
BLAST 2021
June 9-13, 2021
New Mexico State University, Las Cruces, NM, USA
ONLINE
Conference website: https://math.nmsu.edu/blast-2021/
Conference email: blast@nmsu.edu
Submission link: https://easychair.org/conferences/?conf=blast2021
SCOPE
BLAST is a conference series focusing on Boolean Algebras, Lattices, Algebraic Logic, Universal Algebra, Set Theory, Set-theoretic Topology, and Point-free Topology. The series circulates between different universities. The central BLAST web page, with links to past meetings, can be found here: http://math.colorado.edu/blast/
This year's installment of BLAST will take place at New Mexico State University. The scientific program will include invited lectures, tutorial lectures, two special sessions, and contributed talks. Due to the current pandemic, the conference will be entirely online.
INVITED SPEAKERS:
Aichinger, Erhard (Johannes Kepler University Linz)
Carai, Luca (New Mexico State University)
Celani, Sergio (National University of the Center of the Buenos Aires Province)
Fisher, Vera (University of Vienna)
Gehrke, Mai (University of Cote d’Azur, Nice)
Hrusak, Michael (National Autonomous University of Mexico)
Lapenta, Serafina (University of Salerno)
Zamojska-Dzienio, Anna (Warsaw University of Technology)
TUTORIALS:
Bodirsky, Manuel (Dresden University of Technology)
Dow, Alan (UNC Charlotte)
Jung, Achim (University of Birmingham)
SPECIAL SESSIONS:
SPECIAL SESSION IN MEMORY OF W. CHARLES HOLLAND (1935—2020) AND JORGE MARTINEZ (1945—2020)
Organizers: Rick Ball (University of Denver) and Warren McGovern (Florida Atlantic University)
Speakers:
Ball, Rick (University of Denver)
Darnel, Michael (Indiana University South Bend)
Droste, Manfred (University of Leipzig)
Dube, Themba (University of South Africa)
Dvurečenskij, Anatolij (Mathematical Institute, Slovak Academy of Sciences)
Hager, Anthony (Wesleyan University)
Marra, Vincenzo (University of Milan)
McGovern, Warren (Florida Atlantic University)
Schwartz, Niels (University of Passau)
Tsinakis, Constantine (Vanderbilt University)
SPECIAL SESSION ON STONE AND PRIESTLEY DUALITIES
Speakers:
Borlido, Célia (University of Coimbra)
van Gool, Sam (University of Paris)
Holliday, Wesley (UC Berkeley)
Jibladze, Mamuka (Razmadze Mathematical Institute, Tbilisi State University)
Melliès, Paul-André (University of Paris)
Reggio, Luca (University of Oxford)
Salvati, Sylvain (University of Lille)
Tressl, Marcus (University of Manchester)
CONTRIBUTED TALKS:
Abstracts of contributed talks should be submitted through EasyChair:
https://easychair.org/conferences/?conf=blast2021
Please indicate if you would like to submit to a special session. The abstract should not exceed 2 pages.
IMPORTANT DATES:
11 April, 2021: Deadline for submitting abstracts of contributed talks
25 April, 2021: Notification of acceptance
9 June, 2021: Start of the conference
13 June, 2021: End of the conference
LOCAL ORGANIZING COMMITTEE:
Albee, Kempton (grad student)
Bezhanishvili, Guram
Carai, Luca (grad student)
Harding, John
Morandi, Pat
Olberding, Bruce
Peinado, Miguel (grad student)
Raviprakash, Ranjitha (grad student)
Shapirovsky, Ilya
Sinclaire, Morgan (grad student)
Tagged: Erhard Aichinger, Luca Carai, Sergio Celani, Vera Fisher, Mai Gehrke, Michael Hrusak, Serafina Lapenta, Anna Zamojska-Dzienio, Manuel Bodirsky, Alan Dow, Achim Jung, Rick Ball, Michael Darnel, Manfred Droste, Themba Dube, Anatolij Dvurečenskij, Anthony Hager, Vincenzo Marra, Warren McGovern, Niels Schwartz, Constantine Tsinakis, Célia Borlido, Sam van Gool, Wesley Holliday, Mamuka Jibladze, Paul-André Melliès, Luca Reggio, Sylvain Salvati, Marcus Tressl
Two events on February 2
Carnegie Mellon Logic Seminar
1/16/2021 10:43:13
TUESDAY, February 2, 2021
Mathematical logic seminar: 3:30 P.M., Online, Anush Tserunyan, McGill
University
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Ergodic theorems along trees
ABSTRACT: In the classical pointwise ergodic theorem for a probability measure
preserving (pmp) transformation $T$, one takes averages of a given integrable
function over the intervals $\{x, T(x), T^2(x), \hdots, T^n(x)\}$ in front of
the point $x$. We prove a “backward” ergodic theorem for a countable-to-one pmp
$T$, where the averages are taken over subtrees of the graph of T that are
rooted at $x$ and lie behind $x$ (in the direction of $T^{-1}$). Surprisingly,
this theorem yields forward ergodic theorems for countable groups, in
particular, one for pmp actions of free groups of finite rank, where the
averages are taken along subtrees of the standard Cayley graph rooted at the
identity. This strengthens Bufetov’s theorem from 2000, which was the most
general result in this vein. This is joint work with Jenna Zomback.
TUESDAY, February 2, 2021
Set Theory Reading Group: 4:30 P.M., Online, Jenna Zomback, University of
Illinois at Urbana-Champaign
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Ergodic theorems along trees: the proofs
ABSTRACT: In this continuation of the previous talk, we discuss a backward
(inverse) ergodic theorem for a probability measure preserving (pmp)
transformation $T$, where the averages are taken over subtrees of the graph of
$T$ that are rooted at $x$ and lie behind $x$ (in the direction of $T^{-1}$).
We will derive from it a new (forward) pointwise ergodic theorem for pmp
actions of free groups of finite rank, where the averages are taken along
subtrees of the standard Cayley graph rooted at the identity. We will then
discuss a very short proof (due to Tserunyan) of the classical pointwise
ergodic theorem, and, using this proof as an outline, we will sketch the proof
of the backward ergodic theorem. This is joint work with Anush Tserunyan.
Two talks next week (January 22nd)
Toronto Set Theory Seminar
1/15/2021 18:29:14
There was a Typo in the last email. Here the correction:
Speaker:Dima Sinapova, UIC, University of Illinois at Chicago, University of Illinois, Chicago
Date and Time: Friday, January 22, 2021 - 11am to 12:30pm
Location: Online
Abstract: (In previous email)
Speaker: Marcos Mazari Armida, Carnagie Mellon University
Date and Time: Friday, January 22, 2021 - 1:30pm to 3pm
Title: Universal models in classes of abelian groups and modules
Abstract: (In previous email)
To start the semester we will have two talks: one at 11 am (Toronto time) and another at 1 30 pm (Toronto time).
Please use the following link and fill the form (every week) to
enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
Speaker:Dima Sinapova, UIC, University of Illinois at Chicago, University of Illinois, Chicago
Date and Time: Friday, January 22, 2021 - 11am to 12:30pm
Location: Online
Abstract:
Two classical results of Magidor are: (1) from large cardinals it is consistent to have reflection at
$\aleph_{\omega+1}$ and (2) from large cardinals it is consistent to have the failure of SCH at $\aleph_{\omega}$.
These principles are at odds with each other. The former is a
compactness type principle. (Compactness is the phenomenon where if a
certain property holds for every smaller substructure of an object, then
it holds for the entire object.) In contrast, failure of SCH is an
instance of incompactness. The natural question is whether we can have
both of these simultaneously. We show the answer is yes.
We describe a Prikry style iteration, and use it to force stationary
reflection in the presence of not SCH. Then we obtain this situation at
$\aleph_{\omega}$
. This is joint work with Alejandro Poveda and Assaf Rinot.
Speaker: Marcos Mazari Armida, Carnagie Mellon University
Date and Time: Friday, January 22, 2021 - 11am to 12:30pm
Title: Universal models in classes of abelian groups and modules
Abstract:
The search for universal models began in the early twentieth century when Hausdorff showed that there is a universal linear order of
cardinality $\aleph_{n+1}$ if $2^{\aleph_n}= \aleph_{n + 1}$, i.e., a
linear order $U$ of cardinality $\aleph_{n+1}$ such that every linear order of cardinality $\aleph_{n+1}$ embeds in $U$. In this talk, we will
study universal models in several classes of abelian groups and modules
with respect to pure embeddings. In particular, we will present a
complete solution below $\aleph_\omega$, with the exception of
$\aleph_0$ and $\aleph_1$, to Problem 5.1 in page 181 of \emph{Abelian
Groups} by L\'{a}szl\'{o} Fuchs, which asks to find the cardinals
$\lambda$ such that there is a universal abelian p-group for purity of
cardinality $\lambda$. The solution presented will use both
model-theoretic and set-theoretic ideas.
To start the semester we will have two talks: one at 11 am (Toronto time) and another at 1 30 pm (Toronto time).
Please use the following link and fill the form (every week) to
enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
Speaker:Dima Sinapova, UIC, University of Illinois at Chicago, University of Illinois, Chicago
Date and Time: Friday, January 22, 2021 - 11am to 12:30pm
Location: Online
Abstract:
Two classical results of Magidor are: (1) from large cardinals it is consistent to have reflection at
$\aleph_{\omega+1}$ and (2) from large cardinals it is consistent to have the failure of SCH at $\aleph_{\omega}$.
These principles are at odds with each other. The former is a
compactness type principle. (Compactness is the phenomenon where if a
certain property holds for every smaller substructure of an object, then
it holds for the entire object.) In contrast, failure of SCH is an
instance of incompactness. The natural question is whether we can have
both of these simultaneously. We show the answer is yes.
We describe a Prikry style iteration, and use it to force stationary
reflection in the presence of not SCH. Then we obtain this situation at
$\aleph_{\omega}$
. This is joint work with Alejandro Poveda and Assaf Rinot.
Speaker: Marcos Mazari Armida, Carnagie Mellon University
Date and Time: Friday, January 22, 2021 - 11am to 12:30pm
Title: Universal models in classes of abelian groups and modules
Abstract:
The search for universal models began in the early twentieth century when Hausdorff showed that there is a universal linear order of
cardinality $\aleph_{n+1}$ if $2^{\aleph_n}= \aleph_{n + 1}$, i.e., a
linear order $U$ of cardinality $\aleph_{n+1}$ such that every linear order of cardinality $\aleph_{n+1}$ embeds in $U$. In this talk, we will
study universal models in several classes of abelian groups and modules
with respect to pure embeddings. In particular, we will present a
complete solution below $\aleph_\omega$, with the exception of
$\aleph_0$ and $\aleph_1$, to Problem 5.1 in page 181 of \emph{Abelian
Groups} by L\'{a}szl\'{o} Fuchs, which asks to find the cardinals
$\lambda$ such that there is a universal abelian p-group for purity of
cardinality $\lambda$. The solution presented will use both
model-theoretic and set-theoretic ideas.
(KGRC) research seminar talk on Thursday, January 14
Kurt Godel Research Center
1/11/2021 11:46:24
Research seminar
Kurt Gödel Research Center
Thursday, January 14
"Infinitary combinatorics and strong homology"
Jeffrey Bergfalk (KGRC)
Motivated by several recent advances, we will provide a research history
of the main set-theoretic problems arising in the study of strong
homology. As such, this talk will overlap with one on the same theme given
in Paris-Lyon Logic Seminar last fall. We will presume no awareness in our
audience either of strong homology or of that talk, but will aim in this
one to provide, along with the necessary background, some sketch of the
main ideas behind several recent arguments. This is an area in which
simplicial principles and infinitary combinatorics come together. Its
questions, at heart, have tended to be questions about higher-dimensional
variants of classical set-theoretic concerns (like nontrivial coherence,
$\Delta$ systems, etc.); these questions, in turn, increasingly appear to
be of some interest in their own right.
Time and Place
Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not
received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
Barcelona Set theory Seminar
Barcelona Logic Seminar
1/11/2021 2:50:42
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Trevor M. Wilson (Miami Univ.)
TITLE: The large cardinal strength of Vopenka's Principle for trees and for
rayless trees
TIME: January 13 at 16:00 (CET)
PLACE: The Seminar will take place online at the following address:
Logic Seminar at NUS on Wednesday 13 Jan 2021 17:00 hrs - World Logic Day Special
NUS Logic Seminar
1/10/2021 23:33:48
Dear colleagues,
This week's Logic Seminar on Wed 13 January 2021 at 17:00 hrs is an
open session where, in light of the World Logic Day on Thursday, everyone
is encouraged to give a 5 to 10 minutes presentation about his favourate
result or results of his own work. In the case that you have no slides
for this, feel free to share a Word file and type into it on Zoom.
The result can be from any time where you have been working on logic,
it should give the statement and contribution of the theorem. If you
want to give a longer talk, we will schedule one in the next weeks.
Best regards, Frank
Here again the details:
Wednesday 13 Jan 2021 17:00 hrs Singapore Time (+800)
World Logic Seminar Special - Share your nicest results
Discussion via Zoom:
https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
You might reply with a short email to Frank Stephan (fstephan@comp.nus.edu.sg)
and Yang Yue (matyangy@nus.edu.sg) if you follow our request for a short talk
of 5 to 10 minutes, just for planning purposes.
Best regards, Frank
(KGRC) research seminar talk on Thursday, December 17
Kurt Godel Research Center
12/14/2020 10:27:53
Research seminar
Kurt Gödel Research Center
Thursday, December 17
"Ramsey-like Operators"
Peter Holy (University of Udine, Italy)
Starting from measurability upwards, larger large cardinals are usually
characterized by the existence of certain elementary embeddings of the
universe, or dually, the existence of certain ultrafilters. However, below
measurability, we have a somewhat similar picture when we consider certain
embeddings with set-sized domain, or ultrafilters for small collections of
sets. I will present some new results, and also review some older ones, showing
that not only large cardinals below measurability, but also several related
concepts can be characterized in such a way, and I will also provide a sample
application of these characterizations.
Time and Place
Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not
received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
Barcelona Set Theory Seminar
Barcelona Logic Seminar
12/14/2020 2:36:18
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Victoria Gitman (CUNY)
TITLE: Characterizing large cardinals via abstract logics
TIME: December 16 at 16:00 (CET)
PLACE: The Seminar will take place online at the following address:
The coming week is final exams at CUNY, which will be followed by our winter break. This will be the last edition of "This Week in Logic" until the New Year. Have a happy holiday season!
Date and Time: Wednesday December 16, 2020, 1:00 - 2:30 PM. ***NOTICE THE SPECIAL TIME***, on Zoom.
Title: A functorial characterization of classical and quantum entropies.
Abstract: Entropy appears as a useful concept in a wide variety of academic disciplines. As such, one would suspect that category theory would provide a suitable language to encompass all or most of these definitions. The Shannon entropy has recently been given a characterization as a certain affine functor by Baez, Fritz, and Leinster. This characterization is the only characterization I know of that uses linear assumptions (as opposed to additive, exponential, logarithmic, etc). Here, we extend that characterization to include the von Neumann entropy as well as highlight the new categorical structures that arise when trying to do so. In particular, we introduce Grothendieck fibrations of convex categories, and we review the notion of a disintegration, which is a key part of conditional probability and Bayesian statistics and plays a crucial role in our characterization theorem. The characterization of Baez, Fritz, and Leinster interprets Shannon entropy in terms of the information loss associated to a deterministic process, which is possible since the entropy difference associated to such a process is always non-negative. This fails for quantum entropy, and has important physical consequences.
Philog Seminar Thursday, December 17, 6:30 PM EST Barbara H. Partee, Department of Linguistics, University of Massachusetts Amherst Language and Logic: Ideas and Controversies in the History of Formal Semantics (As a very senior and accomplished linguist she is the right person to tell us about formal semantics.)
Brief abstract: The history of formal semantics and pragmatics over the last 50 years is a story of collaboration among linguists, logicians, and philosophers. Since this talk is for a seminar in philosophy, logic, and games, and I’m a linguist, I’ll emphasize aspects of the pre-history and history of formal semantics that concern the relation between language and logic, not presupposing knowledge of linguistics.
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
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(KGRC) research seminar talk on Thursday, December 10
Kurt Godel Research Center
12/7/2020 10:26:42
Research seminar
Kurt Gödel Research Center
Thursday, December 10
"Invariant Ideal Axiom"
Michael Hrušák (UNAM, Mexico City, Mexico)
We shall introduce a consistent set-theoretic axiom which has a profound impact
on convergence properties in topological groups. As an application we show that
consistently (consequence of IIA) every countable sequential group is either
metrizable or $k_\omega$.
Time and Place
Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not
received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
This Week in Logic at CUNY
This Week in Logic at CUNY
12/6/2020 22:22:28
This Week in Logic at CUNY:
- - - - Monday, Dec 7, 2020 - - - -
Logic and Metaphysics Workshop Date: Monday, December 7, 4.15-6.15 (NY time) For meeting information, please email: yweiss@gradcenter.cuny.edu Jennifer McDonald (CUNY)
Title: Essential Structure and Apt Causal Models
Abstract: A promising account of actual causation – the causal relation holding between two token events – uses the language of structural equation models (SEMs). Such an account says, roughly, that actual causation holds between two token events when there is a suitable model according to which (1) the two events occur; and (2) intervening on the model to change the value of the variable that represents the cause changes the value of the variable that represents the effect (Halpern & Pearl, 2005; Hitchcock, 2001; Weslake, 2015; Woodward, 2003). Of course, this calls for an account of when a model is suitable – or, apt. Although initially bracketed, this issue is increasingly pressing; in part due to the recently discovered problem of structural isomorphs (Hall 2007; Hitchcock 2007a; Blanchard and Schaffer 2017; Menzies 2017). This paper offers a unified analysis of two aptness requirements from the literature – those enjoining us to include essential structure and avoid unstable models. While successfully invoked by Blanchard and Schaffer (2017) to resolve the problem of structural isomorphs, these requirements are unilluminating as they stand. My paper synthesizes them into a single aptness requirement that, I claim, gets to the heart of what’s representationally required of a causal model for capturing actual causation.
- - - - Tuesday, Dec 8, 2020 - - - -
- - - - Wednesday, Dec 9, 2020 - - - -
Models of Peano Arithmetic (MOPA) The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Wednesday, Dec 9, 3pm Konrad Zdanowski, Cardinal Stefan Wyszynski University in Warsaw
Truth predicate for Δ0Δ0 formulas and PSPACE computations
We consider a bounded arithmetic in Buss's language enriched with a predicate Tr which is assumed to be a truth definition for bounded sentences. Among other things we assume polynomial induction for Σb1(Tr)Σ1b(Tr) formulas. We show that such an arithmetic captures PSPACE. We prove a witnessing theorem for such an arithmetic by an interpretation of free-cuts free proofs of strict Σ1,b1Σ11,b in U1,∗2U21,∗, a canonical second order arithmetic capturing PSPACE. It follows that the problem of the existence of a truth definition for Δ0Δ0 sentences without the totality of expexp might be more about separating subexponential time alternation hierarchies from PSPACE.
The presentation is based on the following article: Konrad Zdanowski, Truth definition for Δ0Δ0 formulas and PSPACE computations, Fundamenta Mathematicae 252(2021) , 1-38.
Speaker: Dan Shiebler, Oxford University. Date and Time: Wednesday December 9, 2020, 7:00 - 8:30 PM., on Zoom. Title: Functorial Manifold Learning and Overlapping Clustering.
Abstract: We adapt previous research on functorial clustering and topological unsupervised learning to develop a functorial perspective on manifold learning algorithms. Our framework characterizes a manifold learning algorithm in terms of the loss function that it optimizes, which allows us to focus on the algorithm's objective rather than the details of the learning process. We demonstrate that we can express several state of the art manifold learning algorithms, including Laplacian Eigenmaps, Metric Multidimensional Scaling, and UMAP, as functors in this framework. This functorial perspective allows us to reason about the invariances that these algorithms preserve and prove refinement bounds on the kinds of loss functions that any such functor can produce. Finally, we experimentally demonstrate how this perspective enables us to derive and analyze novel manifold learning algorithms.
- - - - Thursday, Dec 10, 2020 - - - -
- - - - Friday, Dec 11, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Dec 11, 11am
The seminar will take place virtually at 11am US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Dima Sinapova, University of Chicago
Iteration, reflection, and singular cardinals
There is an inherent tension between stationary reflection and the failure of the singular cardinal hypothesis (SCH). The former is a compactness type principle that follows from large cardinals. Compactness is the phenomenon where if a certain property holds for every smaller substructure of an object, then it holds for the entire object. In contrast, failure of SCH is an instance of incompactness.
Two classical results of Magidor are: (1) from large cardinals it is consistent to have reflection at ℵω+1ℵω+1, and (2) from large cardinals it is consistent to have the failure of SCH at ℵωℵω.
As these principles are at odds with each other, the natural question is whether we can have both. We show the answer is yes.
We describe a Prikry style iteration, and use it to force stationary reflection in the presence of not SCH. Then we obtain this situation at ℵωℵω by interleaving collapses. This is joint work with Alejandro Poveda and Assaf Rinot.
Date and Time: Wednesday December 16, 2020, 1:00 - 2:30 PM. ***NOTICE THE SPECIAL TIME***, on Zoom.
Title: A functorial characterization of classical and quantum entropies.
Abstract: Entropy appears as a useful concept in a wide variety of academic disciplines. As such, one would suspect that category theory would provide a suitable language to encompass all or most of these definitions. The Shannon entropy has recently been given a characterization as a certain affine functor by Baez, Fritz, and Leinster. This characterization is the only characterization I know of that uses linear assumptions (as opposed to additive, exponential, logarithmic, etc). Here, we extend that characterization to include the von Neumann entropy as well as highlight the new categorical structures that arise when trying to do so. In particular, we introduce Grothendieck fibrations of convex categories, and we review the notion of a disintegration, which is a key part of conditional probability and Bayesian statistics and plays a crucial role in our characterization theorem. The characterization of Baez, Fritz, and Leinster interprets Shannon entropy in terms of the information loss associated to a deterministic process, which is possible since the entropy difference associated to such a process is always non-negative. This fails for quantum entropy, and has important physical consequences.
The next Set Theory in the UK workshop will take place online on Friday, 4 December 2020, from 9.30am-2pm.
Please see the meeting's website http://www1.maths.leeds.ac.uk/~pmtadb/STUK6/STUK6.html for more information.
How to participate: Information how to obtain a login will be available on the conference website soon. Please find this information in advance, on the day before the meeting.
09.30-09.55 Yair Hayut (Hebrew University of Jerusalem): Generics via ultrapowers
10.00-10.50 Arno Pauly (Swansea University): Luzin's (N) and randomness reflection
11.00-11.50 Peter Holy (University of Udine): Ramsey-like operators
lunch break
13.30-13.55 Jiachen Yuan (University of East Anglia): Indestructibility of supercompactness and large cardinals
Titles and abstracts:
Yair Hayut: Generics via ultrapowers
Bukovský and Dehornoy observed (independently) that there is a generic for the Prikry forcing over the iterated ultrapower by the measure. I will show how one can use this fact in order to derive (without referring to the forcing) many interesting properties of the generic extension.
Arno Pauly: Luzin's (N) and randomness reflection
Peter Holy: Ramsey-like operators
Starting from measurability upwards, larger large cardinals are usually characterized by the existence of certain elementary embeddings of the universe, or dually, the existence of certain ultrafilters. However, below measurability, we have a somewhat similar picture when we consider certain embeddings with set-sized domain, or ultrafilters for small collections of sets. I will present some new results, and also review some older ones, showing that not only large cardinals below measurability, but also several related concepts can be characterized in such a way, and I will also provide a sample application of these characterizations.
Jiachen Yuan: Indestructibility of supercompactness and large cardinals
It is well known that "there is a supercompact cardinal which is immune to any $\kappa-$directed closed set forcing" is relatively consistent with "there is a supercompact cardinal". We also know that there is no analogue of such a theorem to any large cardinal stronger than extendible. In fact, provably in $ZFC$ such large cardinal properties will be destroyed by any $\kappa-$directed closed set forcing. For larger cardinals, according to a theorem of Usuba, they can not survive in any set-forcing extension which is not equivalent to a small forcing. However, it was not known if it is possible to have such a large cardinal notion with its supercompactness indestructible. It turns out that this is true for a lot of large cardinals by forcing from a ground model with the same strength.
See you at the meeting!
Andrew Brooke-Taylor, Asaf Karagila and Philipp Schlicht
Tagged: Yair Hayut, Arno Pauly, Peter Holy, Jiachen Yuan
Talk this Friday 2 hours-long (1 30 pm Toronto time)
Toronto Set Theory Seminar
11/30/2020 13:27:39
Hello all,
This week:
Date: Friday December 4, 1.30pm(2 hours long)
location: Online
Please use the following link and fill the form (every week) to enter
the meeting. This form helps the Field Institute to know statistical
data about attendance.
Affiliation: Department of Mathematics, The University of Pittsburgh
Title: The Abraham-Rubin-Shelah Open Coloring Axiom with a Large
Continuum
Abstract:
Open Coloring Axioms may be viewed as consistent generalizations of
Ramsey's Theorem to $\omega_1$ in which topological restrictions are
placed on the colorings. The first of these, denoted
$\mathsf{OCA}_{ARS}$, appeared in the 1985 paper by Abraham, Rubin, and
Shelah. There the authors showed that $\mathsf{OCA}_{ARS}$ is consistent
with $\mathsf{ZFC}$. To ensure that the posets which add the homogeneous
sets satisfy the c.c.c., they construct a type of ``diagonalization"
object (for a continuous coloring $\chi$) called a \emph{Preassignment
of Colors}, which guides the forcing to add the $\chi$-homogeneous sets.
However, the only known constructions of effective preassignments
require the $\mathsf{CH}$. Since a forcing iteration of $\aleph_1$-sized
posets all of whose proper initial segments satisfy the $\mathsf{CH}$
results in a model in which $2^{\aleph_0}$ is at most $\aleph_2$, this
leads naturally to the question of whether $\mathsf{OCA}_{ARS}$ is
consistent, say, with $2^{\aleph_0}=\aleph_3$.
In joint work with Itay Neeman, we answer this question in the
affirmative. In light of the $\mathsf{CH}$ obstacle, we only construct
names for preassignments with respect to a small class $\mathcal{A}$ of
$\mathsf{CH}$-preserving iterations. However, our preassignments are
powerful enough to work even over models in which the $\mathsf{CH}$
fails.
Our final forcing is built by combining the members of $\mathcal{A}$
into a new type of forcing, called a \emph{Partition Product}. A
partition product is a type of restricted memory iteration with
isomorphism and coherent-overlap conditions on the memories. In
particular, each ``memory" is isomorphic to a member of $\mathcal{A}$.
In this talk, we will describe in some detail the definition of a
Partition Product. We will then discuss how to construct more general
preassignments than those used by Abraham, Rubin, and Shelah, gesturing
at the end towards the full construction which we use for our theorem.
========================================
Speaker Bio:
I am a Visiting Assistant Professor in the department of Mathematics at
the University of Pittsburgh, having graduated from UCLA in the Fall of
2019 under the supervision of Itay Neeman. I am interested in questions
about what combinatorial principles determine the size of the continuum,
as well as in questions about the tension between compactness and
incompactness principles in set theory. I reside in Pittsburgh with my
wife, Marian (who is a philosopher of physics), with our indefatigable
toddler Zoe, and with our two cats.
Research seminar
Kurt Gödel Research Center
Thursday, December 3
"On logics that make a bridge from the Discrete to the Continuous"
Mirna Džamonja
(CNRS & Panthéon Sorbonne, Paris, France and Czech Academy of Sciences, Prague)
The talk starts with a surveys of some recent connections between logic
and discrete mathematics. Then we discuss logics which model the passage
between an infinite sequence of finite models to an uncountable limiting
object, such as is the case in the context of graphons. Of particular
interest is the connection between the countable and the uncountable
object that one obtains as the union versus the combinatorial limit of the
same sequence. We compare such logics and discuss some consequences of
such comparisons, as well as some hopes for further results in this
research project.
Time and Place
Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not
received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
This Week in Logic at CUNY
This Week in Logic at CUNY
11/29/2020 21:56:09
This Week in Logic at CUNY:
- - - - Monday, Nov 23, 2020 - - - -
Logic and Metaphysics Workshop Date: Monday, November 23, 4.15-6.15 (NY time) For meeting information, please email: yweiss@gradcenter.cuny.edu Behnam Zolghadr (LMU Munich)
Title: How to Abū Hāšim Meinong
Abstract: Similar to Meinong, Abū Hāšim al-Ǧubbāī (d.933), an Islamic theologian/philosopher, held the view that some objects do not exist. This paper is a comparative study between Meinong’s object theory and Abū Hāšim’s theory of nonexistent objects. Our comparative study will be carried out through three main topics: the characterization principle, objecthood, and the ontological status of existence itself. Moreover, Abū Hāšim and his followers argue that the view that some objects do not exist implies some truth value gaps and/or gluts. We will also discuss two of these arguments.
- - - - Tuesday, Nov 24, 2020 - - - -
Computational Logic Seminar
Tuesday November 24, 2-4pm Ask Sergei Artemov for the (usual) link, unless you already have it.
Speaker: Stepan Kuznetsov, Steklov Mathematical Institute, Russian Academy of Sciences
Title:Ad hoc algebraic models for non-standard Kleene stars
Abstract: Kleene iteration, or Kleene star, is one of the most intriguing algebraic operations appearing in theoretical computer science. In most conventional models, the Kleene star a* is interpreted as the union (limit) of n-th powers of a. In relational structures, this corresponds to reflexive-transitive closure, in language models it is iteration of languages, and so on. Such interpretation of the Kleene star is called *-continuous. However, the usual axiomatization of the Kleene star using induction principles (as opposed to the omega-rule), is essentially weaker and, thus, admits a broader class of models. Existence of nonstandard, non-*-continuous models can be easily proved non-constructively. However, in order to use such models for studying substructural logics with Kleene star one has to construct them explicitly. In this talk, we show two of such models, constructed for proving some facts about derivability in extensions of the Lambek calculus with the Kleene star. Both models are ad hoc algebraic constructions, and we do not yet know whether they could fit in a natural family of models.
The talk is based on my AiML 2018 and AiML 2020 papers
- - - - Wednesday, Nov 25, 2020 - - - -
- - - - Thursday, Nov 26, 2020 - - - -
THANKSGIVING RECESS
- - - - Friday, Nov 27, 2020 - - - -
THANKSGIVING RECESS
Next Week in Logic at CUNY:
- - - - Monday, Nov 30, 2020 - - - -
Logic and Metaphysics Workshop Date: Monday, November 30, 4.15-6.15 (NY time) For meeting information, please email: yweiss@gradcenter.cuny.edu
Mircea Dumitru (Bucharest)
Title: A Free Logic for Fictionalism
Abstract: In Reference without Referents, Mark Sainsbury aims to provide an account of reference that honours the common-sense view that sentences containing empty names like “Sherlock Holmes”, “Vulcan”, and “Santa Claus” are entirely intelligible, and that many such sentences — “Vulcan doesn’t exist”, “Many children believe that Santa Claus will give them presents at Christmas”, etc.— are literally true. Sainsbury’s account endorses the Davidsonian program in the theory of meaning, and combines this with a commitment to Negative Free Logic, which holds that all simple sentences containing empty names are false. In my talk, I pose a number of problems for this account. In particular, I question the ability of Negative Free Logic to make appropriate sense of the truth of familiar sentences containing empty names, including negative existential claims like “Vulcan doesn’t exist”.
Note: this is based on joint work with Frederick Kroon (Auckland).
- - - - Tuesday, Dec 1, 2020 - - - -
Computational Logic Seminar
Tuesday December 1, 2-4pm Ask Sergei Artemov for the (usual) link, unless you already have it.
Speaker: Rohit Parikh, Brooklyn College and CUNY Graduate Center Title: TOPOLOGY AND EPISTEMIC LOGIC
Abstract. We present the main ideas behind a number of logical systems for reasoning about points and sets that incorporate knowledge-theoretic ideas, and also the main results about them. Some of our discussions will be about applications of modal ideas to topology, and some will be on applications of topological ideas in modal logic, especially in epistemic logic.
In the former area, we would like to present the basic ideas and results of topologic, the study of two-sorted bimodal logical systems interpreted on subset spaces; these are arbitrary sets with collections of subsets called opens. Many of the papers in this field deal with questions of axiomatizing the logics of particular classes of subset spaces determined by conditions on the “opens”, such as being closed under intersection, being topologies, or satisfying various chain conditions.
Work in this area has been done by RP as well as Larry Moss (Indiana), Andrew Dabrowski (Indiana), K Georgatos (CUNY), Angela Weiss (CUNY), Chris Steinsvold (CUNY), Bernhard Heinemann (Hagen), Can Baskent (CUNY) and many others.
- - - - Wednesday, Dec 2, 2020 - - - -
- - - - Thursday, Dec 3, 2020 - - - -
- - - - Friday, Dec 4, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Dec 4, 3pm
The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Zach Norwood, University of Michigan
TBA
Next Week in Logic at CUNY:
- - - - Monday, Dec 7, 2020 - - - -
Logic and Metaphysics Workshop Date: Monday, December 7, 4.15-6.15 (NY time) For meeting information, please email: yweiss@gradcenter.cuny.edu Jennifer McDonald (CUNY)
Title: Essential Structure and Apt Causal Models
Abstract: A promising account of actual causation – the causal relation holding between two token events – uses the language of structural equation models (SEMs). Such an account says, roughly, that actual causation holds between two token events when there is a suitable model according to which (1) the two events occur; and (2) intervening on the model to change the value of the variable that represents the cause changes the value of the variable that represents the effect (Halpern & Pearl, 2005; Hitchcock, 2001; Weslake, 2015; Woodward, 2003). Of course, this calls for an account of when a model is suitable – or, apt. Although initially bracketed, this issue is increasingly pressing; in part due to the recently discovered problem of structural isomorphs (Hall 2007; Hitchcock 2007a; Blanchard and Schaffer 2017; Menzies 2017). This paper offers a unified analysis of two aptness requirements from the literature – those enjoining us to include essential structure and avoid unstable models. While successfully invoked by Blanchard and Schaffer (2017) to resolve the problem of structural isomorphs, these requirements are unilluminating as they stand. My paper synthesizes them into a single aptness requirement that, I claim, gets to the heart of what’s representationally required of a causal model for capturing actual causation.
- - - - Tuesday, Dec 8, 2020 - - - -
- - - - Wednesday, Dec 9, 2020 - - - -
- - - - Thursday, Dec 10, 2020 - - - -
- - - - Friday, Dec 11, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Dec 11, 11am
The seminar will take place virtually at 11am US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Dima Sinapova, University of Chicago
TBA
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
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Barcelona Set Theory Seminar
Barcelona Logic Seminar
11/29/2020 5:10:28
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Toby Meadows (UC Irvine)
TITLE: What set theory could not be
TIME: December 2 at 16:00 (CET)
PLACE: The Seminar will take place online at the following address:
Please use the following link and fill the form (every week) to
enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
The study of inner models was initiated by Gödel’s analysis of the constructible universe L
.
Later, it became necessary to study canonical inner models with large
cardinals, e.g. measurable cardinals, strong cardinals or Woodin
cardinals, which were introduced by Jensen, Mitchell, Steel, and others.
Around the same time, the study of infinite two-player games was driven
forward by Martin’s proof of analytic determinacy from a measurable
cardinal, Borel determinacy from ZFC, and Martin and Steel’s proof of
levels of projective determinacy from Woodin cardinals with a measurable
cardinal on top. First Woodin and later Neeman improved the result in
the projective hierarchy by showing that in fact the existence of a
countable iterable model, a mouse, with Woodin cardinals and a top
measure suffices to prove determinacy in the projective hierarchy.
This opened up the possibility for an optimal result stating the
equivalence between local determinacy hypotheses and the existence of
mice in the projective hierarchy, just like the equivalence of analytic
determinacy and the existence of x♯
for every real x
which was shown by Martin and Harrington in the 70’s. The existence of
mice with Woodin cardinals and a top measure from levels of projective
determinacy was shown by Woodin in the 90’s. Together with his earlier
and Neeman’s results this estabilishes a tight connection between
descriptive set theory in the projective hierarchy and inner model
theory.
In this talk, we will outline some of the main results connecting
determinacy hypotheses with the existence of mice with large cardinals
and discuss a number of more recent results in this area.
Please use the following link and fill the form (every week) to
enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
The study of inner models was initiated by Gödel’s analysis of the constructible universe L
.
Later, it became necessary to study canonical inner models with large
cardinals, e.g. measurable cardinals, strong cardinals or Woodin
cardinals, which were introduced by Jensen, Mitchell, Steel, and others.
Around the same time, the study of infinite two-player games was driven
forward by Martin’s proof of analytic determinacy from a measurable
cardinal, Borel determinacy from ZFC, and Martin and Steel’s proof of
levels of projective determinacy from Woodin cardinals with a measurable
cardinal on top. First Woodin and later Neeman improved the result in
the projective hierarchy by showing that in fact the existence of a
countable iterable model, a mouse, with Woodin cardinals and a top
measure suffices to prove determinacy in the projective hierarchy.
This opened up the possibility for an optimal result stating the
equivalence between local determinacy hypotheses and the existence of
mice in the projective hierarchy, just like the equivalence of analytic
determinacy and the existence of x♯
for every real x
which was shown by Martin and Harrington in the 70’s. The existence of
mice with Woodin cardinals and a top measure from levels of projective
determinacy was shown by Woodin in the 90’s. Together with his earlier
and Neeman’s results this estabilishes a tight connection between
descriptive set theory in the projective hierarchy and inner model
theory.
In this talk, we will outline some of the main results connecting
determinacy hypotheses with the existence of mice with large cardinals
and discuss a number of more recent results in this area.
(KGRC) research seminar talk on Thursday, November 26
Kurt Godel Research Center
11/23/2020 9:54:24
Research seminar
Kurt Gödel Research Center
Thursday, November 26
"Convergence of Borel measures and filters on omega"
Damian Sobota (KGRC)
The celebrated Josefson--Nissenzweig theorem asserts, under certain
interpretations, that for every infinite compact space K there exists a
sequence of normalized signed Borel measures on K which converges to 0 with
respect to every continuous real-valued function (i.e. the corresponding
integrals converge to 0). We showed that in the case of products of two
infinite compact spaces K and L one can construct such a sequence of measures
with an additional property that every measure has finite support---let us call
such a sequence ``an fsJN-sequence'' (i.e. a finitely supported
Josefson--Nissenzweig sequence). We then studied the case when the spaces K and
L are only pseudocompact and we proved in ZFC that if the product of K and L is
pseudocompact, then it also admits an fsJN-sequence. On the other hand, we
showed that under the Continuum Hypothesis, or Martin's axiom, or even some
weaker set-theoretic assumptions concerning weak P-points, there exists a
pseudocompact space X such that its square is not pseudocompact and it does not
admit any fsJN-sequences. During my talk I will discuss these as well as other
results concerning the topic and obtained during a joint work with various
combinations of J. Kakol, W. Marciszewski and L. Zdomskyy.
Time and Place
Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not
received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
This Week in Logic at CUNY
This Week in Logic at CUNY
11/22/2020 20:32:48
This Week in Logic at CUNY:
- - - - Monday, Nov 23, 2020 - - - -
Logic and Metaphysics Workshop Date: Monday, November 23, 4.15-6.15 (NY time) For meeting information, please email: yweiss@gradcenter.cuny.edu Behnam Zolghadr (LMU Munich)
Title: How to Abū Hāšim Meinong
Abstract: Similar to Meinong, Abū Hāšim al-Ǧubbāī (d.933), an Islamic theologian/philosopher, held the view that some objects do not exist. This paper is a comparative study between Meinong’s object theory and Abū Hāšim’s theory of nonexistent objects. Our comparative study will be carried out through three main topics: the characterization principle, objecthood, and the ontological status of existence itself. Moreover, Abū Hāšim and his followers argue that the view that some objects do not exist implies some truth value gaps and/or gluts. We will also discuss two of these arguments.
- - - - Tuesday, Nov 24, 2020 - - - -
Computational Logic Seminar
Tuesday November 24, 2-4pm Ask Sergei Artemov for the (usual) link, unless you already have it.
Speaker: Stepan Kuznetsov, Steklov Mathematical Institute, Russian Academy of Sciences
Title:Ad hoc algebraic models for non-standard Kleene stars
Abstract: Kleene iteration, or Kleene star, is one of the most intriguing algebraic operations appearing in theoretical computer science. In most conventional models, the Kleene star a* is interpreted as the union (limit) of n-th powers of a. In relational structures, this corresponds to reflexive-transitive closure, in language models it is iteration of languages, and so on. Such interpretation of the Kleene star is called *-continuous. However, the usual axiomatization of the Kleene star using induction principles (as opposed to the omega-rule), is essentially weaker and, thus, admits a broader class of models. Existence of nonstandard, non-*-continuous models can be easily proved non-constructively. However, in order to use such models for studying substructural logics with Kleene star one has to construct them explicitly. In this talk, we show two of such models, constructed for proving some facts about derivability in extensions of the Lambek calculus with the Kleene star. Both models are ad hoc algebraic constructions, and we do not yet know whether they could fit in a natural family of models.
The talk is based on my AiML 2018 and AiML 2020 papers
- - - - Wednesday, Nov 25, 2020 - - - -
- - - - Thursday, Nov 26, 2020 - - - -
THANKSGIVING RECESS
- - - - Friday, Nov 27, 2020 - - - -
THANKSGIVING RECESS
Next Week in Logic at CUNY:
- - - - Monday, Nov 30, 2020 - - - -
Logic and Metaphysics Workshop Date: Monday, November 30, 4.15-6.15 (NY time) For meeting information, please email: yweiss@gradcenter.cuny.edu
Mircea Dumitru (Bucharest)
Title: A Free Logic for Fictionalism
Abstract: In Reference without Referents, Mark Sainsbury aims to provide an account of reference that honours the common-sense view that sentences containing empty names like “Sherlock Holmes”, “Vulcan”, and “Santa Claus” are entirely intelligible, and that many such sentences — “Vulcan doesn’t exist”, “Many children believe that Santa Claus will give them presents at Christmas”, etc.— are literally true. Sainsbury’s account endorses the Davidsonian program in the theory of meaning, and combines this with a commitment to Negative Free Logic, which holds that all simple sentences containing empty names are false. In my talk, I pose a number of problems for this account. In particular, I question the ability of Negative Free Logic to make appropriate sense of the truth of familiar sentences containing empty names, including negative existential claims like “Vulcan doesn’t exist”.
Note: this is based on joint work with Frederick Kroon (Auckland).
- - - - Tuesday, Dec 1, 2020 - - - -
- - - - Wednesday, Dec 2, 2020 - - - -
- - - - Thursday, Dec 3, 2020 - - - -
- - - - Friday, Dec 4, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Dec 4, 3pm
The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Zach Norwood, University of Michigan
TBA
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
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Barcelona Set Theory Seminar
Barcelona Logic Seminar
11/21/2020 11:38:02
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Andrew Brooke-Taylor (Leeds)
TITLE: Categorifying Borel Reducibility
TIME: November 25 at 16:00 (CET)
PLACE: The Seminar will take place online at the following address:
Please use the following link and fill the form (every week) to
enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
Wadge
theory provides an exhaustive analysis of the topological complexity of
the subsets of a zero-dimensional Polish space. Fons van Engelen
pioneered its applications to topology by obtaining a classification of
the zero-dimensional homogeneous Borel spaces (recall that a space X is homogeneous if for all x,y∈X there exists a homeomorphism h:X⟶X such that h(x)=y).
As a corollary, he showed
that all such spaces (apart from trivial exceptions) are in fact
strongly homogeneous (recall that a space X is strongly homogeneous if all non-empty clopen subspaces of X are homeomorphic to each other).
In a joint work with the other members of the “Wadge Brigade”
(namely, Raphaël Carroy and Sandra Müller), we showed that this last
result extends beyond the Borel realm if one assumes AD. We intend to
sketch the proof of this theorem, with a view towards a complete
classification of the zero-dimensional homogeneous spaces under AD.
Please use the following link and fill the form (every week) to enter the meeting. This form helps the Field Institute to know statistical data about attendance.
Wadge
theory provides an exhaustive analysis of the topological complexity of
the subsets of a zero-dimensional Polish space. Fons van Engelen
pioneered its applications to topology by obtaining a classification of
the zero-dimensional homogeneous Borel spaces (recall that a space X is homogeneous if for all x,y∈X there exists a homeomorphism h:X⟶X such that h(x)=y).
As a corollary, he showed that all such spaces (apart from trivial exceptions) are in fact strongly homogeneous (recall that a space X is strongly homogeneous if all non-empty clopen subspaces of X are homeomorphic to each other).
In a joint work with the other members of the “Wadge Brigade”
(namely, Raphaël Carroy and Sandra Müller), we showed that this last
result extends beyond the Borel realm if one assumes AD. We intend to
sketch the proof of this theorem, with a view towards a complete
classification of the zero-dimensional homogeneous spaces under AD.
(KGRC) research seminar talk on Thursday, November 19
Kurt Godel Research Center
11/16/2020 10:41:08
Research seminar
Kurt Gödel Research Center
Thursday, November 19
"Local club condensation in extender models"
Gabriel Fernandes
(Bar-Ilan University, Ramat Gan, Israel)
Local club condensation is a condensation principle defined by Friedman and
Holy. It is a theorem due to Friedman and Holy that local club condensation
holds in most of the extender models that are weakly iterable.
We prove that in any weakly iterable extender model with $\lambda$-indexing,
given a cardinal $\kappa$, the sequence $\langle L_\alpha [E] \mid \alpha <
\kappa^{++} \rangle$ witnesses local club condensation on the interval
$(\kappa^+ , \kappa^{++})$ iff $\kappa$ is not a subcompact cardinal in $L[E]$.
We also prove that if $\kappa$ is subcompact, then there is no sequence
$\langle M_\alpha \mid \alpha < \kappa^{++} \rangle \in L[E]$ with $M_\kappa =
(H_\kappa)^{L[E]}$ and $M_{\kappa^{++}} = (H_{\kappa^{++}})^{L[E]}$ which
witnesses local club condensation in $(\kappa^+ , \kappa^{++})$.
Using the equivalence between subcompact cardinals and $\neg\square_\kappa$,
due to Schimmerling and Zeman, it follows that $\square_\kappa$ holds iff the
sequence $\langle L_\alpha [E] \mid \alpha < \kappa^{++} \rangle$ witnesses
local club condensation on the interval $(\kappa^+ , \kappa^{++})$.
Time and Place
Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not
received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
This Week in Logic at CUNY
This Week in Logic at CUNY
11/15/2020 18:30:13
This Week in Logic at CUNY:
- - - - Monday, Nov 16, 2020 - - - -
Logic and Metaphysics Workshop Date: Monday, November 16, 4.15-6.15 (NY time) For meeting information, please email: yweiss@gradcenter.cuny.edu
Speaker: Nick Stang (Toronto)
Title: Hegel’s Logic as Logic and as Metaphysics
Abstract: In the Encyclopaedia Logic Hegel claims that logic “coincides with” metaphysics (§24). In this talk, I will explain why Hegelian logic (the science of thinking) is identical with metaphysics (the science of being). Along the way, I will also shed light on two of the most obscure aspects of Hegel’s logic: that it involves “movement” and that this movement works by the identification, and resolution, of contradictions.
- - - - Tuesday, Nov 17, 2020 - - - -
Computational Logic Seminar: no meeting on Tuesday November 17
The New York City CategoryTheory Seminar For meeting zoom details email N. Yanofsky.
Speaker: Enrico Ghiorzi, Appalachian State University. Date and Time: Wednesday November 18, 2020, 7:00 - 8:30 PM., on Zoom. Title: Internal enriched categories.
Abstract: Internal categories feature a notion of completeness which is remarkably well behaved. For example, the internal adjoint functor theorem requires no solution set condition. Indeed, internal categories are intrinsically small, and thus immune from the size issues commonly afflicting standard category theory. Unfortuntely, they are not quite as expressive as we would like: for example, there is no internal Yoneda lemma. To increase the expressivity of internal category theory, we define a notion of internal enrichment over an internal monoidal category and develop its theory of completeness. The resulting theory unites the good properties of internal categories with the expressivity of enriched category theory, thus providing a powerful framework to work with.
- - - - Thursday, Nov 19, 2020 - - - -
- - - - Friday, Nov 20, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Nov 20, 3pm
The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Philipp Schlicht University of Vienna The recognisable universe in the presence of measurable cardinals
A set x of ordinals is called recognisable if it is defined, as a singleton, by a formula phi(y) with ordinal parameters that is evaluated in L[y]. The evaluation is always forcing absolute, in contrast to even Sigma_1-formulas with ordinal parameters evaluated in V. Furthermore, this notion is closely related to similar concepts in infinite computation and Hamkins' and Leahy's implicitly definable sets.
It is conjectured that the recognisable universe generated by all recognisable sets is forcing absolute, given sufficient large cardinals. Our goal is thus to determine the recognisable universe in the presence of large cardinals. The new main result, joint with Philip Welch, is a computation of the recognisable universe within the least inner model with infinitely many measurable cardinals.
Next Week in Logic at CUNY:
- - - - Monday, Nov 23, 2020 - - - -
Logic and Metaphysics Workshop Date: Monday, November 23, 4.15-6.15 (NY time) For meeting information, please email: yweiss@gradcenter.cuny.edu Behnam Zolghadr (LMU Munich)
Title: How to Abū Hāšim Meinong
Abstract: Similar to Meinong, Abū Hāšim al-Ǧubbāī (d.933), an Islamic theologian/philosopher, held the view that some objects do not exist. This paper is a comparative study between Meinong’s object theory and Abū Hāšim’s theory of nonexistent objects. Our comparative study will be carried out through three main topics: the characterization principle, objecthood, and the ontological status of existence itself. Moreover, Abū Hāšim and his followers argue that the view that some objects do not exist implies some truth value gaps and/or gluts. We will also discuss two of these arguments.
- - - - Tuesday, Nov 24, 2020 - - - -
- - - - Wednesday, Nov 25, 2020 - - - -
- - - - Thursday, Nov 26, 2020 - - - -
THANKSGIVING RECESS
- - - - Friday, Nov 27, 2020 - - - -
THANKSGIVING RECESS
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Barcelona Set Theory Seminar
Barcelona Logic Seminar
11/15/2020 13:04:08
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Monroe Eskew (Vienna)
TITLE: Uncommon systems of embeddings
TIME: November 18 at 16:00 (CET)
PLACE: The Seminar will take place online at the following address:
Title: Martin's Maximum^++ implies the P_max axiom (*).
Abstract: Forcing axioms spell out the dictum that if a statement can be
forced, then it is already true. The P_max axiom (*) goes beyond that by
claiming that if a statement is consistent, then it is already true.
Here, the statement in question needs to come from a resticted class of
statements, and "consistent" needs to mean "consistent in a strong
sense." It turns out that (*) is actually equivalent to a forcing axiom,
and the proof is by showing that the (strong) consistency of certain
theories gives rise to a corresponding notion of forcing producing a
model of that theory. This is joint work with D. Asperó building upon
earlier work of R. Jensen and (ultimately) Keisler's "consistency
properties."
(KGRC) research seminar talk on Thursday, November 12
Kurt Godel Research Center
11/9/2020 11:39:30
Research seminar
Kurt Gödel Research Center
Thursday, November 12
"Can You Take Komjath's Inaccessible Away?"
Hossein Lamei Ramandi
(University of Toronto, Ontario, Canada)
In this talk we aim to compare Kurepa trees and Aronszajn trees. Moreover, we
talk about the affect of large cardinal assumptions on this comparison. Using
the the method of walks on ordinals, we will show it is consistent with ZFC
that there is a Kurepa tree and every Kurepa tree contains a Souslin subtree,
if there is an inaccessible cardinal. This is stronger than Komjath's theorem
which asserts the same consistency from two inaccessible cardinals. We will
briefly sketch the ideas to prove that our large cardinal assumption is
optimal. If time permits, we talk about the comparison of Kurepa trees and
Aronszajn trees in the presence of no large cardinal.
This is a joint work with Stevo Todorcevic.
Time and Place
Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not
received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
This Week in Logic at CUNY
This Week in Logic at CUNY
11/8/2020 21:50:45
This Week in Logic at CUNY:
- - - - Monday, Nov 9, 2020 - - - -
Logic and Metaphysics Workshop Date: Monday, November 9, 4.15-6.15 (NY time) For meeting information, please email: yweiss@gradcenter.cuny.edu
Eoin Moore (CUNY) Title: Towards a Justification Logic for FDE
Abstract: In this work-in-progress, I aim to develop a justification logic counterpart to first degree entailment. I produce a logic which is an extension of FDE using justification terms. The results are extended to other paraconsistent logics.
Speaker: Daniel Rogozin, Institute for Information Transmission Problems, Russian Academy of Sciences
Title:Categorical and algebraic aspects of the intuitionistic modal logic IEL^-
Abstract: The intuitionistic modal logic IEL^- is a formalisation of intuitionistic beliefs. This logic has been introduced by S. Artemov and T. Protopopescu to provide an intuitionistic view of knowledge agreed with BHK-semantics. One may understand the modal axioms of this logic in computational terms. Such a consideration is of interest for functional programming theory. We construct the modal lambda calculus based Curry-Howard isomorphic to IEL^- and show that this calculus has strong normalisation and Church-Rosser properties. We have a look at categorical semantics of the obtained lambda calculus and see that it is complete with respect to Cartesian closed categories with certain endofunctors.
Algebraically, the IEL^- modality is a prenucleus operator widespread in the theory of locales and point-free topology. We consider predicate extensions of IEL^- (and some similar logics) and provide a sort of Kripke-Joyal semantics for those logics developing several ideas by R. Goldblatt. We show that such intuitionistic predicate modal logics are complete with respect to their cover systems with the Dedekind-MacNeille completion and the representation of Heyting algebras with corresponding operators.
- - - - Wednesday, Nov 11, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Nov 11, 12:00pm
The seminar will take place virtually at 12pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Ali Enayat had asked whether there is a model of Peano arithmetic (PA) that can be represented as ⟨Q,⊕,⊗⟩⟨Q,⊕,⊗⟩, where ⊕⊕ and ⊗⊗ are continuous functions on the rationals QQ. We prove, affirmatively, that indeed every countable model of PA has such a continuous presentation on the rationals. More generally, we investigate the topological spaces that arise as such topological models of arithmetic. The reals RR, the reals in any finite dimension RnRn, the long line and the Cantor space do not, and neither does any Suslin line; many other spaces do; the status of the Baire space is open.
This is joint work with Ali Enayat, myself and Bartosz Wcisło.
- - - - Thursday, Nov 12, 2020 - - - -
- - - - Friday, Nov 13, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Nov 13, 3pm
The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Diana Montoya, University of Vienna Independence and uncountable cardinals
The classical concept of independence, first introduced by Fichtenholz and Kantorovic has been of interest within the study of combinatorics of the subsets of the real line. In particular the study of the cardinal characteristic ii defined as the minimum size of a maximal independent family of subsets of ω.ω. In the first part of the talk, we will review the basic theory, as well as the most important results regarding the independence number. We will also point out our construction of a poset PP forcing a maximal independent family of minimal size which turns out to be indestructible after forcing with a countable support iteration of Sacks forcing.
In the second part, we will talk about the generalization (or possible generalizations) of the concept of independence in the generalized Baire spaces, i.e. within the space κκκκ when κκ is a regular uncountable cardinal and the new challenges this generalization entails. Moreover, for a specific version of generalized independence, we can have an analogous result to the one mentioned in the paragraph above.
This is joint work with Vera Fischer.
Next Week in Logic at CUNY:
- - - - Monday, Nov 16, 2020 - - - -
Logic and Metaphysics Workshop Date: Monday, November 16, 4.15-6.15 (NY time) For meeting information, please email: yweiss@gradcenter.cuny.edu
Speaker: Nick Stang
- - - - Tuesday, Nov 17, 2020 - - - -
- - - - Wednesday, Nov 18, 2020 - - - -
- - - - Thursday, Nov 19, 2020 - - - -
- - - - Friday, Nov 20, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Nov 20, 3pm
The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Philipp Schlicht University of Vienna TBA
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Barcelona Set Theory Seminar
Barcelona Logic Seminar
11/8/2020 15:20:36
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Gabriel Goldberg (UC Berkeley)
TITLE: On the uniqueness of elementary embeddings
TIME: 16:00 (CET)
PLACE: The Seminar will take place online at the following address:
Title: Martin's Maximum^++ implies the P_max axiom (*).
Abstract: Forcing axioms spell out the dictum that if a statement can be
forced, then it is already true. The P_max axiom (*) goes beyond that by
claiming that if a statement is consistent, then it is already true.
Here, the statement in question needs to come from a resticted class of
statements, and "consistent" needs to mean "consistent in a strong
sense." It turns out that (*) is actually equivalent to a forcing axiom,
and the proof is by showing that the (strong) consistency of certain
theories gives rise to a corresponding notion of forcing producing a
model of that theory. This is joint work with D. Asperó building upon
earlier work of R. Jensen and (ultimately) Keisler's "consistency
properties."
Abstract: Wadge theory provides an exhaustive analysis of the
topological complexity of the subsets of a zero-dimensional Polish
space. Fons van Engelen pioneered its applications to topology by
obtaining a classification of the zero-dimensional homogeneous Borel
spaces (recall that a space $X$ is homogeneous if for all $x,y\in X$
there exists a homeomorphism $h:X\longrightarrow X$ such that $h(x)=y$).
As a corollary, he showed that all such spaces (apart from trivial
exceptions) are in fact strongly homogeneous (recall that a space $X$ is
strongly homogeneous if all non-empty clopen subspaces of $X$ are
homeomorphic to each other).
In a joint work with the other members of the “Wadge Brigade” (namely,
Raphaël Carroy and Sandra Müller), we showed that this last result
extends beyond the Borel realm if one assumes AD. We intend to sketch
the proof of this theorem, with a view towards a complete classification
of the zero-dimensional homogeneous spaces under AD.
Title: Definable maximal families of reals in forcing extensions Abstract: Many types of combinatorial, algebraic or measure-theoretic
families of reals, such as mad families, Hamel bases or Vitali sets, can
be framed as maximal independent sets in analytic hypergraphs on Polish
spaces. Their existence is guaranteed by the Axiom of Choice, but
low-projective witnesses ($\mathbf{Delta}^1_2$) were only known to exist
in general in models of the form $L[a]$ for a real $a$. Our main result
is that, after a countable support iteration of Sacks forcing or for
example splitting forcing (a less known forcing adding splitting reals)
over L, every analytic hypergraph on a Polish space has a
$\mathbf{\Delta}^1_2$ maximal independent set. As a corollary, this
solves an open problem of Brendle, Fischer and Khomskii by providing a
model with a $\Pi^1_1$ mif (maximal independent family) while the
independence number $\mathfrak{i}$ is bigger than $\aleph_1$.
Thanks for your patience. Due to technical errors, the zoom link was generated really late. See you soon!!!!!!!!!!!
Logic Seminar 11 Nov 2020 17:00 hrs at NUS by Philipp Schlicht
NUS Logic Seminar
11/5/2020 20:00:42
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 11 Nov 2020, 17:00 hrs
Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Speaker: Philipp Schlicht, University of Vienna
Title: Structural results about Pi^1_1 and Sigma^1_2 sets
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: Similarities between c.e., Pi^1_1 and Sigma^1_2 sets can be
explained by representing Pi^1_1 and Sigma^1_2 sets as c.e. with respect to
a transfinite enumeration procedure. This representation is important for
classical results about Pi^1_1 and Sigma^1_2 sets, but also for recent
results, for instance about randomness at the level of Pi^1_1 by Hjorth and
Nies and structural results about Sigma^1_2 sets by Chong, Wu and Yu.
In the main result, we calculate the lengths of enumerations. More
precisely, we isolate a certain countable ordinal tau and show that the
length of an enumeration of a Pi^1_1 or Sigma^1_2 set either equals omega_1
or is below tau, and tau is optimal. This ordinal has many other
interesting characterisations. For example, we show that tau is the optimal
bound for the countable ranks of wellfounded Sigma^1_2 relations, in
analogy with the Kunen-Martin theorem. We will further touch on related
structural problems such as calculating Borel ranks of Pi^1_1 and Sigma^1_2
Borel sets.
This is joint work with Philip Welch and Merlin Carl.
Matt Foreman: Hilbert's 10th problem for dynamical systems
Boise Logic and Set Theory Seminar
11/4/2020
Please join us for the next meeting of the ELASTIC seminar next Tuesday, November 10, at 3pm. The meeting will take place at https://boisestate.zoom.us/j/98755933038.
Speaker: Matt Foreman (UCI)
Title: Hilbert's 10th problem for dynamical systems
Abstract: A basic problem in smooth dynamics is determining if a system can be distinguished from its inverse, i.e., whether a smooth diffeomorphism T is isomorphic to T^{-1}. We show that this problem is sufficiently general that asking it for particular choices of T is equivalent to the validity of well-known number theoretic conjectures including the Riemann Hypothesis and Goldbach's conjecture. Further one can produce computable diffeomorphisms T such that the question of whether T is isomorphic to T^{-1} is independent of ZFC.
Tagged: Matt Foreman
(KGRC) research seminar talk on Thursday, November 5
Kurt Godel Research Center
11/2/2020 11:16:29
Research seminar
Kurt Gödel Research Center
Thursday, November 5
"On Continuous Tree-Like Scales and related properties of Internally
Approachable structures"
Omer Ben-Neria
(Hebrew University of Jerusalem, Israel)
In his PhD thesis, Luis Pereira isolated and developed several principles
of singular cardinals that emerge from Shelah's PCF theory; principles
which involve properties of scales, such as the inexistence of continuous
Tree-Like scales, and properties of internally approachable structures
such as the Approachable Free Subset Property.
In the talk, we will discuss these principles and their relations, and
present new results from a joint work with Dominik Adolf concerning their
consistency and consistency strength.
Time and Place
Talk at 3:00pm via Zoom:
This talk will be given via Zoom. If you haven't received the meeting link
by the day before the talk, please contact richard.springer@univie.ac.at!
Tagged: Omer Ben-Neria
Logic Seminar 4 Nov 2020 17:00 hrs at NUS by Andre Nies
NUS Logic Seminar
11/2/2020 0:34:00
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 4 Nov 2020, 17:00 hrs
Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Speaker: Andre Nies, University of Auckland
Title: Weak reducibilities on the K-trivial sets
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
Abstract: The K-trivial sets are antirandom in the sense that the
initial segment complexity in terms of prefix-free Kolmogorov
complexity K grows as slowly as possible. Chaitin introduced this
notion in about 1975, and showed that each K-trivial is Turing below
the halting set. Shortly after, Solovay proved that a K-trivial set
can be noncomputable.
In the past two decades, many alternative characterisations of this
class have been found: properties such as being low for K, low for
Martin-Loef (ML) randomness, and a basis for ML randomness, which
state in one way or the other that the set is close to computable.
Initially, the class of noncomputable K-trivials appeared to be
amorphous. More recently, evidence of an internal structure has been
found. Most of these results can be phrased in the language of a
mysterious reducibility on the K-trivials which is weaker than
Turing's: A is ML-below B if each ML-random computing B also computes A.
Bienvenu, Greenberg, Kucera, Nies and Turetsky (JEMS 2016) showed that
there an ML-complete K-trivial set. Greenberg, Miller and Nies (JML,
2019) established a dense hierarchy of subclasses of the K-trivials
based on fragments of Omega computing the set, and each such subclass
is an initial segment for ML. More recent results generalise these
approaches using so-called cost functions. They also show that each
K-trivial set is ML-equivalent to a c.e. K-trivial.
Alternative reducibilities on the K-trivials will be considered near
the end of the talk. One of them is related to the extreme lowness
notion of strong jump traceability, and appears to be orthogonal to
ML-reducibility. Very recent work with Greenberg and Turetsky provides
manyfold characterisations in terms of cost functions, and random oracles.
Tagged: Andre Nies
This Week in Logic at CUNY
This Week in Logic at CUNY
11/1/2020 21:03:08
This Week in Logic at CUNY:
- - - - Monday, Nov 2, 2020 - - - -
Logic and Metaphysics Workshop Date: Monday, November 2, 4.15-6.15 (NY time) For meeting information, please email: yweiss@gradcenter.cuny.edu
Speaker: Heinrich Wansing (Bochum)
Title: A Note on Synonymy in Proof-Theoretic Semantics
Abstract: The topic of identity of proofs was put on the agenda of general (or structural) proof theory at an early stage. The relevant question is: When are the differences between two distinct proofs (understood as linguistic entities, proof figures) of one and the same formula so inessential that it is justified to identify the two proofs? The paper addresses another question: When are the differences between two distinct formulas so inessential that these formulas admit of identical proofs? The question appears to be especially natural if the idea of working with more than one kind of derivations is taken seriously. If a distinction is drawn between proofs and disproofs (or refutations) as primitive entities, it is quite conceivable that a proof of one formula amounts to a disproof of another formula, and vice versa. The paper develops this idea.
- - - - Tuesday, Nov 3, 2020 - - - -
Computational Logic Seminar
Tuesday, Nov 3, 2-4pm
For meeting zoom details please email sartemov@gmail.com. Speaker: Sergei Artemov,Graduate Center CUNY
Title:Justification Awareness Models
Abstract: We offer a new approach in formal epistemology which overcomes some principal deficiencies of Hintikka-style modal epistemic logic such as logical omniscience, a hidden assumption of the common knowledge of the model, missing evidence representation, etc.
In this project, we pursue two principal ideas: (i) justifications are prime objects of epistemic modeling: knowledge and belief are defined evidence-based concepts; (ii) awareness restrictions are applied to justifications rather than to propositions, which allows for the maintaining of desirable closure properties. The basic resulting structures, Justification Awareness Models, JAMs, naturally include major justification models, Kripke models and, in addition, represent situations with multiple possibly fallible justifications which, in full generality, were previously off the scope of rigorous epistemic modeling.
Attachments area
- - - - Wednesday, Nov 4, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Oct 28, 3:00pm
The seminar will take place virtually at 3pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Victoria Gitman, CUNY A model of second-order arithmetic satisfying AC but not DC: Part II
One of the strongest second-order arithmetic systems is full second-order arithmeticZ2Z2 which asserts that every second-order formula (with any number of set quantifiers) defines a set. We can augment Z2Z2 with choice principles such as the choice scheme and the dependent choice scheme. The Σ1nΣn1-choice scheme asserts for every Σ1nΣn1-formula φ(n,X)φ(n,X) that if for every nn, there is a set XX witnessing φ(n,X)φ(n,X), then there is a single set ZZ whose nn-th slice ZnZn is a witness for φ(n,X)φ(n,X). The Σ1nΣn1-dependent choice scheme asserts that every Σ1nΣn1-relation φ(X,Y)φ(X,Y) without terminal nodes has an infinite branch: there is a set ZZ such that φ(Zn,Zn+1)φ(Zn,Zn+1) holds for all nn. The system Z2Z2 proves the Σ12Σ21-choice scheme and the Σ12Σ21-dependent choice scheme. The independence of Π12Π21-choice scheme from Z2Z2 follows by taking a model of Z2Z2 whose sets are the reals of the Feferman-Levy model of ZFZF in which every ℵLnℵnL is countable and ℵLωℵωL is the first uncountable cardinal.
We construct a model of ZF+ACωZF+ACω whose reals give a model of Z2Z2 together with the full choice scheme in which Π12Π21-dependent choice fails. This result was first proved by Kanovei in 1979 and published in Russian. It was rediscovered by Sy Friedman and myself with a slightly simplified proof.
- - - - Thursday, Nov 5, 2020 - - - -
Philog - Seminar in Logic, Games and Philosophy On Thursday, November 5 (6:30 PM) we will return to the book by Diaconis and Skyrms . The Zoom talk will be led by Paul Pedersen. Title: Inverse Inference from Bayes and Laplace to Statistics.
Abstract: You are screening new drugs for a certain disease. Some patients get better by at least a certain amount; some don't. For one new drug, more get better on the drug than on a placebo. How confident should you be of the new drug's effectiveness on the evidence?
Theorem (Mitchell and Schimmerling, submitted for publication) Assume there is no transitive class model of ZFC with a Woodin cardinal. Let νν be a singular ordinal such that ν>ω2ν>ω2 and cf(ν)<|ν|cf(ν)<|ν|. Suppose νν is a regular cardinal in K. Then νν is a measurable cardinal in K. Moreover, if cf(ν)>ωcf(ν)>ω, then oK(ν)≥cf(ν)oK(ν)≥cf(ν).
I will say something intuitive and wildly incomplete but not misleading about the meaning of the theorem, how it is proved, and the history of results behind it.
Next Week in Logic at CUNY:
- - - - Monday, Nov 9, 2020 - - - -
Logic and Metaphysics Workshop Date: Monday, November 9, 4.15-6.15 (NY time) For meeting information, please email: yweiss@gradcenter.cuny.edu
Eoin Moore (CUNY) Title: Towards a Justification Logic for FDE
Abstract: In this work-in-progress, I aim to develop a justification logic counterpart to first degree entailment. I produce a logic which is an extension of FDE using justification terms. The results are extended to other paraconsistent logics.
- - - - Tuesday, Nov 10, 2020 - - - -
- - - - Wednesday, Nov 11, 2020 - - - -
- - - - Thursday, Nov 12, 2020 - - - -
- - - - Friday, Nov 13, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Nov 13, 3pm
The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Diana Montoya, University of Vienna TBA
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
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Seminar next week
Toronto Set Theory Seminar
10/30/2020 15:54:27
Hello everyone,
Here a list for upcoming talk (I had a typo last week,
Ralf Schindle's talk will be the third one in Nov 13th). Links will be provided later.
Nov 6th 1:30 pm
Jonathan Schilhan (University of Vienna, Austria)
Title: Definable maximal families of reals in forcing extensions
Abstract: Many types of combinatorial, algebraic or measure-theoretic
families of reals, such as mad families, Hamel bases or Vitali sets, can
be framed as maximal independent sets in analytic hypergraphs on Polish
spaces. Their existence is guaranteed by the Axiom of Choice, but
low-projective witnesses ($\mathbf{Delta}^1_2$) were only known to exist
in general in models of the form $L[a]$ for a real $a$. Our main result
is that, after a countable support iteration of Sacks forcing or for
example splitting forcing (a less known forcing adding splitting reals)
over L, every analytic hypergraph on a Polish space has a
$\mathbf{\Delta}^1_2$ maximal independent set. As a corollary, this
solves an open problem of Brendle, Fischer and Khomskii by providing a
model with a $\Pi^1_1$ mif (maximal independent family) while the
independence number $\mathfrak{i}$ is bigger than $\aleph_1$.
-----
Nov 13th
11:00 am
Ralf Schindler (University of Münster, Germany)
Title: Martin's Maximum^++ implies the P_max axiom (*).
Abstract: Forcing axioms spell out the dictum that if a statement can be
forced, then it is already true. The P_max axiom (*) goes beyond that by
claiming that if a statement is consistent, then it is already true.
Here, the statement in question needs to come from a resticted class of
statements, and "consistent" needs to mean "consistent in a strong
sense." It turns out that (*) is actually equivalent to a forcing axiom,
and the proof is by showing that the (strong) consistency of certain
theories gives rise to a corresponding notion of forcing producing a
model of that theory. This is joint work with D. Asperó building upon
earlier work of R. Jensen and (ultimately) Keisler's "consistency
properties."
------
Nov 20th
1:30 pm
Andrea Medini (University of Vienna, Austria)
Title: Topological applications of Wadge theory
Abstract: Wadge theory provides an exhaustive analysis of the
topological complexity of the subsets of a zero-dimensional Polish
space. Fons van Engelen pioneered its applications to topology by
obtaining a classification of the zero-dimensional homogeneous Borel
spaces (recall that a space $X$ is homogeneous if for all $x,y\in X$
there exists a homeomorphism $h:X\longrightarrow X$ such that $h(x)=y$).
As a corollary, he showed that all such spaces (apart from trivial
exceptions) are in fact strongly homogeneous (recall that a space $X$ is
strongly homogeneous if all non-empty clopen subspaces of $X$ are
homeomorphic to each other).
In a joint work with the other members of the “Wadge Brigade” (namely,
Raphaël Carroy and Sandra Müller), we showed that this last result
extends beyond the Borel realm if one assumes AD. We intend to sketch
the proof of this theorem, with a view towards a complete classification
of the zero-dimensional homogeneous spaces under AD.
Title: Reflection properties at successors of singulars.
Abstract: We
survey some recent advances in techniques for getting reflection
properties at successors of singulars with particular attention to the
tree property and stationary reflection
(KGRC) research seminar talk on Thursday, October 29
Kurt Godel Research Center
10/26/2020 11:51:12
Research seminar
Kurt Gödel Research Center
Thursday, October 29
"Structural reflection and shrewd cardinals"
Philipp Lücke
(University of Barcelona, Spain)
In my talk, I want to present work dealing with the interplay between Time
and Place extensions of the \emph{Downward Löwenheim–Skolem Theorem} to
strong logics, large cardinal axioms and set-theoretic reflection
principles, focussing on the characterization of large cardinal notions
through model- and set-theoretic reflection properties. The work of
Bagaria and his collaborators shows that various important objects in the
middle and upper reaches of the large cardinal hierarchy can be
characterized through principles of \emph{structural reflection}. I will
discuss recent results dealing with possible characterizations of notions
from the lower part of this hierarchy through the principle
$\mathrm{SR}^-$, introduced by Bagaria and Väänänen. These results show
that the principle $\mathrm{SR}^-$ is closely connected to the notion of
\emph{shrewd cardinals}, introduced by Rathjen in a proof-theoretic
context, and embedding characterizations of these cardinals that resembles
Magidor's classical characterization of supercompactness.
Time and Place
This talk will be given via Zoom. If you haven't received the meeting link
by the day before the talk, please contact richard.springer@univie.ac.at!
Tagged: Philipp Lücke
Toronto Set Theory Seminar (First talk of this Term)
Toronto Set Theory Seminar
10/25/2020 11:17:04
Hello Everyone,
The Toronto Set Theory seminar will finally start this semester. The organizer will be organized by two post-docs, ad tradition dictates: David Schrittesser (U-Toronto, cc'ed) and me (Ivan Ongay-Valverde,
York).
The first talk of the semester will be given by Spencer Unger who recently moved to Toronto. After that, we will have weekly talks. The second talk will be given by
Ralf Schindler from Münste. Here the information:
Title:
Reflection properties at successors of singulars.
Abstract:
We survey some recent advances in techniques for getting reflection
properties at successors of singulars with particular attention to the
tree property and stationary reflection
For the second talk
Speaker:
Ralf Schindler
Time and link: Nov 6, 202011:00 AM
Eastern Time (US and Canada, i.e.
Toronto time
)
Logic and Metaphysics Workshop Date: Monday, October 26th, 4.15-6.15 (NY time) For meeting information, please email: yweiss@gradcenter.cuny.edu
Speaker: Lisa Warenski (CUNY)
Title: The Metaphysics of Epistemic Norms
Abstract: A metanormative theory inter alia gives an account of the objectivity of normative claims and addresses the ontological status of normative properties in its target domain. A metanormative theory will thus provide a framework for interpreting the claims of its target first-order theory. Some irrealist metanormative theories (e.g., Gibbard 1990 and Field 2000, 2009) conceive of normative properties as evaluative properties that may attributed to suitable objects of assessment (doxastic states, agents, or actions) in virtue of systems of norms. But what are the conditions for the acceptability of systems of norms, and relatedly, correctness of normative judgment? In this paper, I take up these questions for epistemic norms. Conditions for the acceptability of epistemic norms, and hence correctness of epistemic judgment, will be based on the critical evaluation of norms for their ability to realize our epistemic aims and values. Epistemic aims and values, in turn, are understood to be generated from the epistemic point of view, namely the standpoint of valuing truth.
Title:Justification Logics as Internal Languages -- Part 2 of 2
Abstract:
In this talk the justification logic J- is shown to correspond to the internal language of a class of categories. In addition to proving soundness and completeness, we will show that the categorical models and the basic models are in correspondence, and that one can be transformed into the other in a straightforward way.
- - - - Wednesday, Oct 28, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Oct 28, 3:00pm
The seminar will take place virtually at 3pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Victoria Gitman, CUNY A model of second-order arithmetic satisfying AC but not DC
One of the strongest second-order arithmetic systems is full second-order arithmeticZ2Z2 which asserts that every second-order formula (with any number of set quantifiers) defines a set. We can augment Z2Z2 with choice principles such as the choice scheme and the dependent choice scheme. The Σ1nΣn1-choice scheme asserts for every Σ1nΣn1-formula φ(n,X)φ(n,X) that if for every nn, there is a set XX witnessing φ(n,X)φ(n,X), then there is a single set ZZ whose nn-th slice ZnZn is a witness for φ(n,X)φ(n,X). The Σ1nΣn1-dependent choice scheme asserts that every Σ1nΣn1-relation φ(X,Y)φ(X,Y) without terminal nodes has an infinite branch: there is a set ZZ such that φ(Zn,Zn+1)φ(Zn,Zn+1) holds for all nn. The system Z2Z2 proves the Σ12Σ21-choice scheme and the Σ12Σ21-dependent choice scheme. The independence of Π12Π21-choice scheme from Z2Z2 follows by taking a model of Z2Z2 whose sets are the reals of the Feferman-Levy model of ZFZF in which every ℵLnℵnL is countable and ℵLωℵωL is the first uncountable cardinal.
We construct a model of ZF+ACωZF+ACω whose reals give a model of Z2Z2 together with the full choice scheme in which Π12Π21-dependent choice fails. This result was first proved by Kanovei in 1979 and published in Russian. It was rediscovered by Sy Friedman and myself with a slightly simplified proof.
- - - - Thursday, Oct 29, 2020 - - - -
Seminar in Logic, Games and Philosophy
Zoom seminar, Thursday October 29 at 6:30 PM
Cailin O'Connor, UC Irvine
Title: Measuring Conventionality
Abstract: Standard accounts of convention include notions of arbitrariness. But many have conceived of conventionality as an all or nothing affair. In this paper, I develop a framework for thinking of conventions as coming in degrees of arbitrariness. In doing so, I introduce an information theoretic measure intended to capture the degree to which a solution to a certain social problem could have been otherwise. As the paper argues, this framework can help improve explanation aimed at the cultural evolution of social traits. Good evolutionary explanations recognize that most functional traits are also conventional, at least to some degree, and vice versa.
The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Benedikt Löwe, University of Hamburg TBA
Workshop on Substructural Logics, Hierarchies Thereof, and Solutions to the Liar
The Logic and Metaphysics Workshop and the Saul Kripke Center are hosting a day of talks on substructural Logics, hierarchies thereof, and solutions to the Liar on Friday, October 30, 2020. The schedule, NY time, will be as follows (abstracts can be accessed here):
10.00. Strict/Tolerant and Tolerant/Strict Logics, Melvin Fitting, CUNY. 11.40. Expressibility and the (Un)paradoxicality Paradoxes, Will Nava, NYU. 1.20. Lunch Break. 2.00. What is Meta-inferential Validity?, Chris Scambler, NYU. 3.40. Supervaluations and the Strict-Tolerant Hierarchy, Brian Porter, CUNY. 5.20. End (virtual gathering).
Talks will be on Zoom, and are open to all interested. A link will be sent out on the mailing lists of the Logic and Metaphysics Workshop and the Saul Kripke Center the day before. People not on either of those lists who want to receive the link should email Graham Priest (priest DOT graham AT gmail DOT com). PLEASE FEEL FREE TO PASS ON THIS ANNOUNCEMENT.
Next Week in Logic at CUNY:
- - - - Monday, Nov 2, 2020 - - - -
Logic and Metaphysics Workshop Date: Monday, November 2, 4.15-6.15 (NY time) For meeting information, please email: yweiss@gradcenter.cuny.edu
Speaker: Lisa Warenski (CUNY). Title: The Metaphysics of Epistemic Norms
Abstract: A metanormative theory inter alia gives an account of the objectivity of normative claims and addresses the ontological status of normative properties in its target domain. A metanormative theory will thus provide a framework for interpreting the claims of its target first-order theory. Some irrealist metanormative theories (e.g., Gibbard 1990 and Field 2000, 2009) conceive of normative properties as evaluative properties that may attributed to suitable objects of assessment (doxastic states, agents, or actions) in virtue of systems of norms. But what are the conditions for the acceptability of systems of norms, and relatedly, correctness of normative judgment? In this paper, I take up these questions for epistemic norms. Conditions for the acceptability of epistemic norms, and hence correctness of epistemic judgment, will be based on the critical evaluation of norms for their ability to realize our epistemic aims and values. Epistemic aims and values, in turn, are understood to be generated from the epistemic point of view, namely the standpoint of valuing truth.
- - - - Tuesday, Nov 3, 2020 - - - -
- - - - Wednesday, Nov 4, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Oct 28, 3:00pm
The seminar will take place virtually at 3pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Victoria Gitman, CUNY A model of second-order arithmetic satisfying AC but not DC: Part II
One of the strongest second-order arithmetic systems is full second-order arithmeticZ2Z2 which asserts that every second-order formula (with any number of set quantifiers) defines a set. We can augment Z2Z2 with choice principles such as the choice scheme and the dependent choice scheme. The Σ1nΣn1-choice scheme asserts for every Σ1nΣn1-formula φ(n,X)φ(n,X) that if for every nn, there is a set XX witnessing φ(n,X)φ(n,X), then there is a single set ZZ whose nn-th slice ZnZn is a witness for φ(n,X)φ(n,X). The Σ1nΣn1-dependent choice scheme asserts that every Σ1nΣn1-relation φ(X,Y)φ(X,Y) without terminal nodes has an infinite branch: there is a set ZZ such that φ(Zn,Zn+1)φ(Zn,Zn+1) holds for all nn. The system Z2Z2 proves the Σ12Σ21-choice scheme and the Σ12Σ21-dependent choice scheme. The independence of Π12Π21-choice scheme from Z2Z2 follows by taking a model of Z2Z2 whose sets are the reals of the Feferman-Levy model of ZFZF in which every ℵLnℵnL is countable and ℵLωℵωL is the first uncountable cardinal.
We construct a model of ZF+ACωZF+ACω whose reals give a model of Z2Z2 together with the full choice scheme in which Π12Π21-dependent choice fails. This result was first proved by Kanovei in 1979 and published in Russian. It was rediscovered by Sy Friedman and myself with a slightly simplified proof.
- - - - Thursday, Nov 5, 2020 - - - -
- - - - Friday, Nov 6, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Oct 30, 3pm
The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
(KGRC) research seminar talk on Thursday, October 22
Kurt Godel Research Center
10/19/2020 10:55:49
Research seminar
Kurt Gödel Research Center
Thursday, October 22
"Tree forcings, sharps and absoluteness"
Philipp Schlicht (KGRC)
In joint results with Fabiana Castiblanco from 2018, we showed that
several classical tree forcings preserve sharps for reals and levels of
projective determinacy, and studied their impact on definable equivalence
relations (in particular, the question whether they add equivalence
classes to thin projective equivalence relations). I will discuss these
results and natural open problems on tree forcings and absoluteness that
arise from them.
Time and Place
This talk will be given via Zoom. If you haven't received the meeting link
by the day before the talk, please contact richard.springer@univie.ac.at!
Tagged: Philipp Schlicht
Barcelona Set Theory Seminar
Barcelona Logic Seminar
10/19/2020 9:21:05
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
The Seminar will take place at the following address:
Logic and Metaphysics Workshop Date: Monday, October 19th, 4.15-6.15 (NY time) For meeting information, please email: yweiss@gradcenter.cuny.edu
Michael Glanzberg (Rutgers)
Title: Models, Model Theory, and Modeling
Abstract: In this paper, I shall return to the relations between logic and semantics of natural language. My main goal is to advance a proposal about what that relation is. Logic as used in the study of natural language—an empirical discipline—functions much like specific kinds of scientific models. Particularly, I shall suggest, logics can function like analogical models. More provocatively, I shall also suggest they can function like model organisms often do in the biological sciences, providing a kind of controlled environment for observations. My focus here will be on a wide family of logics that are based on model theory, so in the end, these claims apply equally to model theory itself. Along the way towards arguing for my thesis about models in science, I shall also try to clarify the role of model theory in logic. At least, I shall suggest, it can play distinct roles in each domain. It can offer something like scientific models when it comes to empirical applications, while at the same time furthering conceptual analysis of a basic notion of logic.
Speakers:Pavel Naumov (King's College, Pennsylvania) and Rui-Jie Yew (Scripps College, California)
Title:An Epistemic Logic of Desire
Abstract: We say that an agent desires a condition phi if (1) the agent knows neither that phi is true nor that phi is false (2) among all indistinguishable worlds, she prefers those in which phi is true. In this talk, I will propose a sound and complete logical system that describes the interplay between the desire and the knowledge modalities in the multiagent setting.
- - - - Wednesday, Oct 21, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Oct 21, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Roman Kossak, CUNY Types, gaps, and pairs of models of PA, Part III
The talk will be a survey of results on first-order theories of pairs (N,M), where M is a model of PA and N is its elementary extension, under various assumptions on the models and on the type of extension. In particular, I will discuss in detail the results on countable recursively saturated models and their cofinal submodels from a joint paper with Jim Schmerl.
The New York City Category Theory Seminar Speaker: Andrei V. Rodin, Saint Petersburg State University. Date and Time: Wednesday October 21, 2020, 7:00 - 8:30 PM., on Zoom.
The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Gabriel Goldberg, University of Berkeley
Ultrapowers and the approximation property
Countably complete ultrafilters are the combinatorial manifestation of strong large cardinal axioms, but many of their basic properties are undecidable no matter the large cardinal axioms one is willing to adopt. The Ultrapower Axiom (UA) is a set theoretic principle that permits the development of a much clearer picture of countably complete ultrafilters and, consequently, the large cardinals from which they derive. It is not known whether UA is (relatively) consistent with very large cardinals, but assuming there is a canonical inner model with a supercompact cardinal, the answer should be yes: this inner model should satisfy UA and yet inherit all large cardinals present in the universe of sets. The predicted resemblance between the large cardinal structure of this model and that of the universe itself is so extreme as to suggest that certain consequences of UA must in fact be provable outright from large cardinal axioms. While the inner model theory of supercompact cardinals remains a major open problem, this talk will describe a technique that already permits a number of consequences of UA to be replicated from large cardinals alone. Still, the technique rests on the existence of inner models that absorb large cardinals, but instead of building canonical inner models, one takes ultrapowers.
Next Week in Logic at CUNY:
- - - - Monday, Oct 26, 2020 - - - -
- - - - Tuesday, Oct 27, 2020 - - - -
- - - - Wednesday, Oct 28, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Oct 28, 2:00pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Victoria Gitman, CUNY A model of second-order arithmetic satisfying AC but not DC
One of the strongest second-order arithmetic systems is full second-order arithmeticZ2Z2 which asserts that every second-order formula (with any number of set quantifiers) defines a set. We can augment Z2Z2 with choice principles such as the choice scheme and the dependent choice scheme. The Σ1nΣn1-choice scheme asserts for every Σ1nΣn1-formula φ(n,X)φ(n,X) that if for every nn, there is a set XX witnessing φ(n,X)φ(n,X), then there is a single set ZZ whose nn-th slice ZnZn is a witness for φ(n,X)φ(n,X). The Σ1nΣn1-dependent choice scheme asserts that every Σ1nΣn1-relation φ(X,Y)φ(X,Y) without terminal nodes has an infinite branch: there is a set ZZ such that φ(Zn,Zn+1)φ(Zn,Zn+1) holds for all nn. The system Z2Z2 proves the Σ12Σ21-choice scheme and the Σ12Σ21-dependent choice scheme. The independence of Π12Π21-choice scheme from Z2Z2 follows by taking a model of Z2Z2 whose sets are the reals of the Feferman-Levy model of ZFZF in which every ℵLnℵnL is countable and ℵLωℵωL is the first uncountable cardinal.
We construct a model of ZF+ACωZF+ACω whose reals give a model of Z2Z2 together with the full choice scheme in which Π12Π21-dependent choice fails. This result was first proved by Kanovei in 1979 and published in Russian. It was rediscovered by Sy Friedman and myself with a slightly simplified proof.
- - - - Thursday, Oct 29, 2020 - - - -
- - - - Friday, Oct 30, 2020 - - - -
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
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Logic Seminar 21 Oct 2020 17:00 hrs at NUS by Rupert Hoelzl (Universitaet der Bundeswehr Muenchen)
NUS Logic Seminar
10/15/2020 5:12:52
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 21 Oct 2020, 17:00 hrs
Talk via Zoom:
https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Speaker: Rupert Hoelzl, Universitaet der Bundeswehr Muenchen
Title: Monte Carlo Computability
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
We introduce Monte Carlo computability as a probabilistic concept of
computability on infinite objects and prove that Monte Carlo
computable functions are closed under composition. We then mutually
separate the following classes of functions from each other: the class
of multi-valued functions that are non-deterministically computable,
that of Las Vegas computable functions, and that of Monte Carlo
computable functions. We give natural examples of computational
problems witnessing these separations. As a specific problem
which is Monte Carlo computable but neither Las Vegas computable
nor non-deterministically computable, we study the problem of
sorting infinite sequences that was recently introduced by
Neumann and Pauly. Their results allow us to draw conclusions
about the relation between algebraic models and Monte Carlo computability.
Logic Seminar 28 Oct 2020 17:00 hrs at NUS by Liao Luke
NUS Logic Seminar
10/15/2020 5:00:58
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 28 Oct 2020, 17:00 hrs
Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Speaker: Liao Luke
Title: Computability of Julia sets
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: TTE-computable is one of the major definitions of computable real
functions. We focus on a generalisation of TTE and check the basic
cases of computability of Julia sets. We prove quadratic polynomials
with Siegel disc incomputable in TTE is still incomputable in generalisation.
Logic Seminar 28 Oct 2020 17:00 hrs at NUS by Liao Yuke (typing errors corrected)
NUS Logic Seminar
10/15/2020 5:03:04
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 28 Oct 2020, 17:00 hrs
Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Speaker: Liao Yuke
Title: Computability of Julia sets
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: TTE-computable is one of the major definitions of computable real
functions. We focus on a generalisation of TTE and check the basic
cases of computability of Julia sets. We prove quadratic polynomials
with Siegel disc incomputable in TTE is still incomputable in generalisation.
(KGRC) research seminar talk on Thursday, October 15
Kurt Godel Research Center
10/12/2020 11:19:04
The KGRC welcomes as guest:
Ziemowit Kostana (host: Noé de Rancourt) will visit from October 15 to October
20, 2020 and give a talk (see below).
* * *
Research seminar
Kurt Gödel Research Center
Thursday, October 15
"Fraïssé theory, and forcing absoluteness of rigidity for linear orders"
Ziemowit Kostana
(University of Warsaw, Poland)
During the talk I would like to introduce the theory of Cohen-like
first-order structures. These are countable or uncountable structures
which are "generic" much in the same sense as the Cohen reals. They can be
added to the universe of set theory using finite or, say, countable
conditions and exhibit different properties. I will focus on the
construction of a rigid linear order, whose rigidity is absolute for ccc
extensions.
Time and Place
This talk will be given via Zoom. If you haven't received the meeting link
by the day before the talk, please contact richard.springer@univie.ac.at!
This Week in Logic at CUNY
This Week in Logic at CUNY
10/11/2020 22:23:20
This Week in Logic at CUNY:
- - - - Monday, Oct 12, 2020 - - - -
Logic and Metaphysics Workshop Date: Monday, October 12th, 4.15-6.15 (NY time) For meeting information, please email: yweiss@gradcenter.cuny.edu Brian Cross Porter (CUNY). Title: A Metainferential Hierachy of Validity Curry Paradoxes
Abstract: The validity curry paradox is a paradox involving a validity predicate which does not use any of the logical connectives; triviality can be derived using only the structural rules of Cut and Contraction with intuitively plausible rules for the validity predicate. This has been used to argue that we should move to a substructural logic dropping Cut or Contraction. In this talk, I’ll present metainferential versions of the validity curry paradox. We can recreate the validity curry paradox at the metainferential level, the metametainferential level, the metametametainferential level, and so on ad infinitum. I argue that this hierarchy of metaninferential validity curry paradoxes poses a problem for the standard substructural solutions to the validity curry paradox.
Abstract: Imagine a database—a set of propositions Γ = {F1, . . . , Fn} with some kind of probability estimates and let a proposition X logically follow from Γ . What is the best justified lower bound of the probability of X? The traditional approach, e.g. within Adams’ probability logic, computes the numeric lower bound for X corresponding to the worst-case scenario. We suggest a more flexible parameterized approach by assuming probability events u1, u2, . . . , un that support Γ and calculating aggregated evidence e(u1, u2, . . . , un) for X. The probability of e provides a tight lower bound for any, not only a worst-case, situation. The problem is formalized in a version of justification logic and the conclusions are supported by corresponding completeness theorems. This approach can handle conflicting and inconsistent data and allows the gathering both positive and negative evidence for the same proposition.
- - - - Wednesday, Oct 14, 2020 - - - -
The New York City Category Theory Seminar
Speaker: Jonathon Funk, Queensborough CUNY. Date and Time: Wednesday October 14, 2020, 6:00 - 7:30PM (NOTICE DIFFERENT TIME) on Zoom.
For meeting zoom details email N. Yanofsky. Title: Pseudogroup Torsors.
Abstract: We use sheaf theory to analyze the topos of etale actions on the germ groupoid of a pseudogroup in the sense that we present a site for this topos, which we call the classifying topos of the pseudogroup. Our analysis carries us further into how pseudogroup morphisms and geometric morphisms are related. Ultimately, we shall see that the classifying topos classifies what we call a pseudogroup torsor. In hindsight, we see that pseudogroups form a bicategory of `flat' bimodules.
Joint work with Pieter Hofstra.
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Oct 14, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Roman Kossak, CUNY Types, gaps, and pairs of models of PA, Part II
The talk will be a survey of results on first-order theories of pairs (N,M), where M is a model of PA and N is its elementary extension, under various assumptions on the models and on the type of extension. In particular, I will discuss in detail the results on countable recursively saturated models and their cofinal submodels from a joint paper with Jim Schmerl.
- - - - Thursday, Oct 15, 2020 - - - -
- - - - Friday, Oct 16, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Oct 16, 3pm
The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Richard Matthews, University of Leeds
Taking Reinhardt's Power Away
Many large cardinals can be defined through elementary embeddings from the set-theoretic universe to some inner model, with the guiding principle being that the closer the inner model is to the universe the stronger the resulting theory. Under ZFC, the Kunen Inconsistency places a hard limit on how close this can be. One is then naturally led to the question of what theory is necessary to derive this inconsistency with the primary focus having historically been embeddings in ZF without Choice.
In this talk we take a different approach to weakening the required theory, which is to study elementary embeddings from the universe into itself in ZFC without Power Set. We shall see that I1, one of the largest large cardinal axioms not known to be inconsistent with ZFC, gives an upper bound to the naive version of this question. However, under reasonable assumptions, we can reobtain this inconsistency in our weaker theory.
Next Week in Logic at CUNY:
- - - - Monday, Oct 19, 2020 - - - -
Logic and Metaphysics Workshop Date: Monday, October 19th, 4.15-6.15 (NY time) For meeting information, please email: yweiss@gradcenter.cuny.edu
Michael Glanzberg (Rutgers)
Title: Models, Model Theory, and Modeling
Abstract: In this paper, I shall return to the relations between logic and semantics of natural language. My main goal is to advance a proposal about what that relation is. Logic as used in the study of natural language—an empirical discipline—functions much like specific kinds of scientific models. Particularly, I shall suggest, logics can function like analogical models. More provocatively, I shall also suggest they can function like model organisms often do in the biological sciences, providing a kind of controlled environment for observations. My focus here will be on a wide family of logics that are based on model theory, so in the end, these claims apply equally to model theory itself. Along the way towards arguing for my thesis about models in science, I shall also try to clarify the role of model theory in logic. At least, I shall suggest, it can play distinct roles in each domain. It can offer something like scientific models when it comes to empirical applications, while at the same time furthering conceptual analysis of a basic notion of logic.
- - - - Tuesday, Oct 20, 2020 - - - -
- - - - Wednesday, Oct 21, 2020 - - - -
The New York City Category Theory Seminar Speaker: Andrei V. Rodin, Saint Petersburg State University. Date and Time: Wednesday October 21, 2020, 7:00 - 8:30 PM., on Zoom.
Logic Seminar 14 Oct 2020 17:00 hrs at NUS by Tran Chieu-Minh (University of Notre Dame)
NUS Logic Seminar
10/9/2020 1:12:36
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 14 Oct 2020, 17:00 hrs
Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Speaker: Tran Chieu-Minh
Title: Incidence counting and trichotomy in o-minimal structures
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: Zarankiewicz's problem in graph theory asks to determine
the largest possible number of edges |E| in a bipartite graph G =
(V_1, V_2; E) with the parts V_1 and V_2 containing n_1 and n_2
vertices, respectively, and such that G contains no complete bipartite
subgraphs on k vertices. Graphs definable in o-minimal (or more
generally distal structures) enjoy stronger bounds than general
graphs, providing an abstract setting for the Szemeredi-Trotter
theorem and related incidence bounds. We obtain almost optimal upper
and lower bounds for hypergraphs definable in locally modular
o-minimal structures, along with some applications to incidence
counting (e.g. the number of incidences between points and boxes with
axis parallel sides on the plane whose incidence graph is K_{k,k}-free
is almost linear). We explain how the exponent appearing in these
bounds is tightly connected to the trichotomy principle in o-minimal
structures.
Joint work with Abdul Basit, Artem Chernikov, Sergei Starchenko and
Terence Tao.
Link to the Barcelona Set Theory Seminar
Barcelona Logic Seminar
10/6/2020 3:45:39
Dear All,
Just to let you know that the link to the Barcelona Set Theory Seminar is the following:
Clovis Hamel: An introduction to Cp-theory and Grothendieck spaces
Toronto Set Theory Seminar
2/7/2021
Place: Fields Institute (Room 210)
Date: October 11, 2019 (13:30-15:00)
Speaker: Clovis Hamel
Title: An introduction to Cp-theory and Grothendieck spaces
Abstract: This is joint work with Prof. Frank Tall. An old theorem of Grothendieck states that countably compact subspaces of Cp(X) have compact closure whenever X is countably compact. We shall survey some basic results in Cp-theory and then focus on Grothendieck spaces, i.e. those for which the conclusion of Grothendieck theorem holds. Following Arhangel'skiĭ, we shall introduce the Lindelöf Σ-spaces, which belong to a wide class of well-behaved spaces, and prove that they are Grothendieck. We will show a compactness criterion for Fréchet-Urysohn Grothendieck spaces involving exchanging (ultra)limits which is similar to the classical Ptak's lemma. In a later occasion, we shall show the relevance of this results in Model Theory, e.g. the definability of pathological Banach spaces in various continuous logics.
Tagged: Clovis Hamel
(KGRC) research seminar talk on Thursday, October 8
Kurt Godel Research Center
10/5/2020 10:32:50
The KGRC welcomes as guests:
The visit by Jerzy Kąkol (host: Damian Sobota) had to be canceled due to
COVID travel restrictions.
The visit by Colin Jahel (host: Noé de Rancourt), too, had to be canceled
due to COVID travel restrictions; the talk will be given via Zoom (see
below).
Ziemowit Kostana (host: Noé de Rancourt) will visit from October 15 to
October 20, 2020 and give a talk (talk to be announced later).
* * *
Research seminar
Kurt Gödel Research Center
Thursday, October 8
"Actions of automorphism groups of Fraïssé limits on the space of linear
orderings"
Colin Jahel
(Claude Bernard University Lyon 1, France)
In 2005, Kechris, Pestov and Todorčević exhibited a correspondence between
combinatorial properties of structures and dynamical properties of their
automorphism groups. In 2012, Angel, Kechris and Lyons used this
correspondence to show the unique ergodicity of all the actions of some
groups. In this talk, I will give an overview of the aforementioned
results and discuss recent work generalizing results of Angel, Kechris and
Lyons.
Time and Place
Talk at 3:00pm
This talk will be given via Zoom. If you haven't received the meeting link
by the day before the talk, please contact richard.springer@univie.ac.at!
This Week in Logic at CUNY
This Week in Logic at CUNY
10/4/2020 21:34:47
This Week in Logic at CUNY:
- - - - Monday, Oct 5, 2020 - - - -
Logic and Metaphysics Workshop Date: Monday, October 5th, 4.15-6.15 (NY time) For meeting information, please email: yweiss@gradcenter.cuny.edu Speaker: Oliver Marshall (UNAM) Title: Mathematical Information Content
Abstract: Alonzo Church formulated several logistic theories of propositions based on three alternative criteria of identity (1949, 1954, 1989, 1993). The most coarse grained of these criteria is Alternative (2), according to which two propositions are identical iff the sentences that express them are necessarily materially equivalent. Alternative (1) is more discerning. According to Alternative (1), two propositions are identical iff the sentences that express them can be obtained from one another by the substitution of synonyms for synonyms and λ-conversion. Church said that he intended this to limn a notion of proposition closely related to Frege’s notion of gedanke, but added that it will not be sufficiently discerning if propositions in the sense of Alternative (1) are taken as objects of assertion and belief (1993). Alternative (0), the most discerning criterion, says that two propositions are identical iff the sentences that express them can be obtained from one another by the substitution of synonyms for synonyms. I argue that Alternative (1) does indeed provide insight into one of the topics that concerned Frege (1884) – namely, abstraction. Then I discuss various counterexamples to Church’s criteria (including one due to Paul Bernays, 1961). I close by proposing a criterion of identity for mathematical information content based on the various examples under discussion.
Speaker: John Connor, Graduate Center CUNY Title: Justification Logics as Internal Languages -- Part 1 of 2
Abstract: This is the first of two talks in which I answer the question (in the affirmative) of whether the justification logic J is the internal language of a class of categories. In this first talk we will discuss the methods by which a logic may be interpreted in a category, and the properties such interpretations may have. Concrete examples will include propositional intuitionistic logic as the internal language of bi-Cartesian closed categories. Some aspects of the interpretation of higher logics in topoi will also be discussed. Previous knowledge of category theory is not assumed.
The talk concludes with a discussion of the difficulties inherent in the interpretation of justification logics. In the next talk, a class of categories is presented with respect to which the justification logic J is sound and complete in a weak sense.
- - - - Wednesday, Oct 7, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Oct 7, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Roman Kossak, CUNY Types, gaps, and pairs of models of PA
- - - - Thursday, Oct 8, 2020 - - - -
- - - - Friday, Oct 9, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Oct 9, 11am
The seminar will take place virtually at 11am US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Heike Mildenberger, Albert-Ludwigs-Universität Freiburg Forcing with variants of Miller trees
Guzmán and Kalajdzievski introduced a variant of Miller forcing P(F)P(F) that diagonalises a given filter FF over ωω and has Axiom A. We investigate the effect of P(F)P(F) for particularly chosen Canjar filters FF. This is joint work with Christian Bräuninger.
Next Week in Logic at CUNY:
- - - - Monday, Oct 12, 2020 - - - -
Logic and Metaphysics Workshop Date: Monday, October 12th, 4.15-6.15 (NY time) For meeting information, please email: yweiss@gradcenter.cuny.edu Brian Cross Porter (CUNY). Title: A Metainferential Hierachy of Validity Curry Paradoxes
Abstract: The validity curry paradox is a paradox involving a validity predicate which does not use any of the logical connectives; triviality can be derived using only the structural rules of Cut and Contraction with intuitively plausible rules for the validity predicate. This has been used to argue that we should move to a substructural logic dropping Cut or Contraction. In this talk, I’ll present metainferential versions of the validity curry paradox. We can recreate the validity curry paradox at the metainferential level, the metametainferential level, the metametametainferential level, and so on ad infinitum. I argue that this hierarchy of metaninferential validity curry paradoxes poses a problem for the standard substructural solutions to the validity curry paradox.
- - - - Tuesday, Oct 13, 2020 - - - -
- - - - Wednesday, Oct 14, 2020 - - - -
The New York City Category Theory Seminar
Speaker: Jonathon Funk, Queensborough CUNY. Date and Time: Wednesday October 14, 2020, 6:00 - 7:30PM (NOTICE DIFFERENT TIME) on Zoom.
For meeting zoom details email N. Yanofsky. Title: Pseudogroup Torsors.
Abstract: We use sheaf theory to analyze the topos of etale actions on the germ groupoid of a pseudogroup in the sense that we present a site for this topos, which we call the classifying topos of the pseudogroup. Our analysis carries us further into how pseudogroup morphisms and geometric morphisms are related. Ultimately, we shall see that the classifying topos classifies what we call a pseudogroup torsor. In hindsight, we see that pseudogroups form a bicategory of `flat' bimodules.
Joint work with Pieter Hofstra.
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Oct 14, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Roman Kossak, CUNY Types, gaps, and pairs of models of PA
- - - - Thursday, Oct 15, 2020 - - - -
- - - - Friday, Oct 16, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Oct 16, 3pm
The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Richard Matthews, University of Leeds TBA
- - - - Other Logic News - - - -
Ad hoc logic workshop
There is some interesting work going on in NYC at the moment on substructural logics, hierarchies thereof, and solutions to the liar. So we're scheduling an ad hoc workshop on these matters (by Zoom), with talks by Mel Fitting, Will Nava, Brian Porter, and Chris Scambler. It will be on Friday 30th October. The aim will be to have two papers in the morning, and two in the afternoon. Full details will be sent round in due course. This is just an early warning to make a note of the date if you are interested. - Graham Priest
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
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Wednesday seminar
Prague Set Theory Seminar
10/4/2020 15:52:49
Dear all,
Still no seminar the coming Wednesday, October 7th.
Unless there is a major the development, I expect the seminar to resume
on Wednesday October 14th. (The originally scheduled off-site meeting
got cancelled.)
Best,
David
Invitation to Logic Seminar 7 Oct 2020 17:00 hrs at NUS by Wu Guohua
NUS Logic Seminar
10/2/2020 9:28:07
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 7 October 2020, 17:00 hrs
Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Speaker: Wu Guohua
Title: Splittings
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: I will present a survey of splittings in sets and in
degrees. Downey-Stob's long paper in 1993 provides a comprehensive and
updated survey. In this talk, I first recall some classical theorems
on this topic, both ideas and techniques, and following this, I will
present some results along this line being done in the last few years.
Tagged: Wu Guohua
Barcelona Set Theory seminar
Barcelona Set Theory Seminar
10/1/2020 10:59:55
Dear Colleague,
Next week we will start our online Barcelona Set Theory seminar, which will meet every Wednesday at 4:00 (CEST). Please find attached the announcement of the next session. Feel free to distribute it.
If you wish to attend, please send an email to bagaria@ub.edu and we’ll send you the link.
Logic and Metaphysics Workshop Date: Monday, September 21st, 4.15-6.15 (NY time)
For zoom information, email Yale Weiss at: yweiss@gradcenter.cuny.edu. Speaker: Yale Weiss (CUNY) Title: Arithmetical Semantics for Non-Classical Logic
Abstract: I consider logics which can be characterized exactly in the lattice of the positive integers ordered by division. I show that various (fragments of) relevant logics and intuitionistic logic are sound and complete with respect to this structure taken as a frame; different logics are characterized in it by imposing different conditions on valuations. This presentation will both cover and extend previous/forthcoming work of mine on the subject.
- - - - Tuesday, Sep 22, 2020 - - - -
Computational Logic Seminar Time 2:00 - 4:00 PM Tuesday, September 22, 2020 Please send me a request for a link to this talk: (unless you are registered or have already sent me a request for the whole semester). Speaker: Hirohiko Kushida, Graduate Center, City University of New York Title: Reduction of Modal Logic and Realization in Justification Logic
Abstract: In this paper, we first offer basic results on modal logic: (1) a wide range of modal systems can be syntactically reduced to the modal logic K in terms of theoremhood and (2) we can restrict the forms of modal axioms without changing their deductive power in those range of modal logics. Then, based on these results, we offer a new, simple, uniform and modular proof-theoretical proof of the realization of a wide range of modal logics with possible combinations of modal axioms T, D, 4, 5 including S5 in Justification Logic. We do not use a generalization of sequent calculus such as hypersequent and nested sequent calculi. We just utilize the standard cut-free sequent calculus for K and then we show, in the realized proof in Justification Logic (corresponding to K), how to recover the realizations of the modal axioms by rewriting terms in the proof.
- - - - Wednesday, Sep 23, 2020 - - - -
- - - - Thursday, Sep 24, 2020 - - - -
Seminar in Philosophical Logic Thursday, Sep 24, 6:30 PM. (Zoom link upon request RParikh@gc.cuny.edu; will be sent automatically to seminar members) Arthur Paul Pedersen, Department of Computer Science, City College of New York, CUNY Coherent Judgment: Previsions and Forecasts
Abstract. This talk is to continue critical discussion of Persi Diaconis and Brian Skyrms' book chapter, "Judgment," from their Ten Great Ideas about Chance (Princeton University Press, 2018). Specifically, I will cover two variations on coherence advanced by de Finetti to justify his theory of personal probability, each cast in game-theoretic terms — one based on previsions, the other based on forecasting. I will show how his ideas extend both conceptually and mathematically to subsequent developments due to Savage, Anscombe & Aumann, and others. While the talk is to be self-contained, an excellent reference for broader discussion is Peter Fishburn's "Utility and Subjective Probability: Contemporary Theories," International Encyclopedia of the Social & Behavioral Sciences, 2001: 16113-16121.
- - - - Friday, Sep 25, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Sep 25, 11am
The seminar will take place virtually at 11am US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Ralf Schindler, University of Münster Martin's Maximum^++ implies the P_max axiom (*)
Forcing axioms spell out the dictum that if a statement can be forced, then it is already true. The P_max axiom (*) goes beyond that by claiming that if a statement is consistent, then it is already true. Here, the statement in question needs to come from a resticted class of statements, and 'consistent' needs to mean 'consistent in a strong sense.' It turns out that (*) is actually equivalent to a forcing axiom, and the proof is by showing that the (strong) consistency of certain theories gives rise to a corresponding notion of forcing producing a model of that theory. This is joint work with D. Asperó building upon earlier work of R. Jensen and (ultimately) Keisler's 'consistency properties'.
Next Week in Logic at CUNY:
- - - - Monday, Sep 28, 2020 - - - -
Logic and Metaphysics Workshop Date: Monday, September 29st, 4.15-6.15 (NY time)
For zoom information, email Yale Weiss at: yweiss@gradcenter.cuny.edu. Speaker: Daniel Hoek (Virginia Tech) Title: Coin flips, Spinning Tops and the Continuum Hypothesis
Abstract: By using a roulette wheel or by flipping a countable infinity of fair coins, we can randomly pick out a point on a continuum. In this talk I will show how to combine this simple observation with general facts about chance to investigate the cardinality of the continuum. In particular I will argue on this basis that the continuum hypothesis is false. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. A classic theorem from Banach and Kuratowski (1929), tells us that it follows, given the axioms of ZFC, that there are cardinalities between countable infinity and the cardinality of the continuum. (Get the paper here: https://philpapers.org/archive/HOECAT-2.pdf).
- - - - Tuesday, Sep 29, 2020 - - - -
- - - - Wednesday, Sep 30, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Sep 30, 2:00pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Abstract: The usual base theory used in reverse mathematics, RCA0RCA0, is the fragment of second-order arithmetic axiomatized by Δ01Δ10 comprehension and Σ01Σ10 induction. The weaker base theory RCA∗0RCA0∗ is obtained by replacing Σ01Σ10 induction with Δ01Δ10 induction (and adding the well-known axiom expexp in order to ensure totality of the exponential function). In first-order terms, RCA0RCA0 is conservative over IΣ1IΣ1 and RCA∗0RCA0∗ is conservative over BΣ1+expBΣ1+exp.
Some of the most interesting open problems in reverse mathematics concern the first-order strength of statements from Ramsey Theory, in particular Ramsey's Theorem for pairs and two colours. In this talk, I will discuss joint work with Kasia Kowalik, Tin Lok Wong, and Keita Yokoyama concerning the strength of Ramsey's Theorem over RCA∗0RCA0∗.
Given standard natural numbers n,k≥2n,k≥2, let RTnkRTkn stand for Ramsey's Theorem for kk-colourings of nn-tuples. We first show that assuming the failure of Σ01Σ10 induction, RTnkRTkn is equivalent to its own relativization to an arbitrary Σ01Σ10-definable cut. Using this, we give a complete axiomatization of the first-order consequences of RCA∗0+RTnkRCA0∗+RTkn for n≥3n≥3 (this turns out to be a rather peculiar fragment of PA) and obtain some nontrivial information about the first-order consequences of RT2kRTk2. Time permitting, we will also discuss the question whether our results have any relevance for the well-known open problem of characterizing the first-order consequences of RT22RT22 over the traditional base theory RCA0RCA0.
In the first part of the talk, we concentrated on Ramsey's Theorem for nn-tuples where n≥3n≥3. In this second part, the focus will be on RT22RT22.
The New York City Category Theory Seminar Date and Time: Wednesday September 30, 2020, 7:00 - 8:30 PM., on Zoom. Zoom information will be posted on the web page on the day of the talk http://www.sci.brooklyn.cuny.edu/~noson/CTseminar.html
Speaker: David Ellerman, University of Ljubljana. Title: The Logical Theory of Canonical Maps: The Elements & Distinctions Analysis of the Morphisms, Duality, Canonicity, and Universal Constructions in Sets.
Abstract: Category theory gives a mathematical characterization of naturality but not of canonicity. The purpose of this paper is to develop the logical theory of canonical maps based on the broader demonstration that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, canonicity, and universal constructions in Sets, the category of sets and functions. The analysis extends directly to other Sets-based concrete categories (groups, rings, vector spaces, etc.). Elements and distinctions are the building blocks of the two dual logics, the Boolean logic of subsets and the logic of partitions. The partial orders (inclusion and refinement) in the lattices for the dual logics define morphisms. The thesis is that the maps that are canonical in Sets are the ones that are defined (given the data of the situation) by these two logical partial orders and by the compositions of those maps. Paper: Available here http://www.sci.brooklyn.cuny.edu/~noson/Ellerman2020.pdf
- - - - Thursday, Oct 1, 2020 - - - -
- - - - Friday, Oct 2, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Oct 2, 11am
The seminar will take place virtually at 11am US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
David Aspero, University of East Anglia
Martin’s Maximum^++ implies the P_max axiom (*) (Part 2)
This will be a sequel to Ralf Schindler’s talk on 9/25. My plan is to give a reasonably detailed account of the proof of the result in the title.
Next Week in Logic at CUNY:
- - - - Monday, Oct 5, 2020 - - - -
- - - - Tuesday, Oct 6, 2020 - - - -
- - - - Wednesday, Oct 7, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Oct 7, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Roman Kossak, CUNY Types, gaps, and pairs of models of PA
- - - - Thursday, Oct 8, 2020 - - - -
- - - - Friday, Oct 9, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Oct 9, 11am
The seminar will take place virtually at 11am US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
There is some interesting work going on in NYC at the moment on substructural logics, hierarchies thereof, and solutions to the liar. So we're scheduling an ad hoc workshop on these matters (by Zoom), with talks by Mel Fitting, Will Nava, Brian Porter, and Chris Scambler. It will be on Friday 30th October. The aim will be to have two papers in the morning, and two in the afternoon. Full details will be sent round in due course. This is just an early warning to make a note of the date if you are interested. - Graham Priest
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
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Wednesday seminar
Prague Set Theory Seminar
9/27/2020 8:14:24
Dear all,
As the general epidemiological situation remains uncertain, there will
be no seminar next week, Wednesday October 30th.
I expect the seminar to resume during October. (Probably no seminar on
October 14th -- our Institute holds an off-site meeting.)
Best,
David
Logic Seminar 30 Sept 2020 17:00 hrs by Vasco Brattka (Universitaet der Bundeswehr Muenchen)
NUS Logic Seminar
9/23/2020 23:49:10
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 30 September 2020, 17:00 hrs
Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Speaker: Vasco Brattka
Title: The Discontinuity Problem
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract
We discuss the question whether there is a weakest unsolvable
mathematical problem. In recent years the Weihrauch lattice has
been established as a suitable computability theoretic framework
to analyze the uniform computational content of problems from many
different fields of mathematics. Here we answer a question by
Schroeder, whether there is a weakest discontinuous problem with
respect to the continuous version of Weihrauch reducibility.
We introduce the discontinuity problem, and we show that it
is reducible exactly to the effectively discontinuous problems,
defined in a suitable way. However, in which sense this answers
Schroeder's question sensitively depends on the axiomatic framework
that is chosen and it is a positive answer if we work in Zermelo-
Fraenkel set theory with dependent choice and the axiom of determinacy.
On the other hand, using the axiom of choice, one can construct
problems which are discontinuous, but not effectively so.
Hence, the exact structure of the ``bottom'' of the Weihrauch lattice
sensitively depends on the axiomatic setting that we choose.
We prove our result using Wadge games for mathematical problems and
while the existence of a winning strategy for player II characterizes
continuity of the problem (as already shown by Nobrega and Pauly),
the existence of a winning strategy for player I characterizes
effective discontinuity of the problem. We also provide further
insights into the algebraic nature of the discontinuity problem.
For one we show that the parallelization of the discontinuity
problem is exactly the non-computability problem that was studied
before. One the other hand, we introduce a new algebraic operation
in the Weihrauch lattice that we call summation and which is the
dual operation to parallelization. While parallelization can be
seen as an analogue of the bang operator in linear logic, summation
can be seen as an analogue of the question mark operator.
It turns out that the discontinuity problem can be obtained as
summation of a number of well-known problems in the Weihrauch
lattice, such as the (lesser) limited problem of omniscience
and variants thereof. More generally, we study the action of
the monoid formed by parallelization and summation on the
Weihrauch lattice, and we prove that this action can lead to
at most five different Weihrauch degrees, which (in the maximal case)
are always organized in a pentagon. We show that the discontinuity
problem appears as the bottom of several natural such pentagons.
This leads to further interesting characterizations of the
discontinuity problem.
Tagged: Vasco Brattka
UPDATE - This Week in Logic at CUNY
This Week in Logic at CUNY
9/20/2020 22:00:19
Added the talk on Tuesday Sep 22 in the Computational Logic Seminar
-Jonas
This Week in Logic at CUNY:
- - - - Monday, Sep 21, 2020 - - - -
Logic and Metaphysics Workshop Date: Monday, September 21st, 4.15-6.15 (NY time)
For zoom information, email Yale Weiss at: yweiss@gradcenter.cuny.edu. Speaker: Yale Weiss (CUNY) Title: Arithmetical Semantics for Non-Classical Logic
Abstract: I consider logics which can be characterized exactly in the lattice of the positive integers ordered by division. I show that various (fragments of) relevant logics and intuitionistic logic are sound and complete with respect to this structure taken as a frame; different logics are characterized in it by imposing different conditions on valuations. This presentation will both cover and extend previous/forthcoming work of mine on the subject.
- - - - Tuesday, Sep 22, 2020 - - - -
Computational Logic Seminar Time 2:00 - 4:00 PM Tuesday, September 22, 2020 Please send me a request for a link to this talk: (unless you are registered or have already sent me a request for the whole semester). Speaker: Hirohiko Kushida, Graduate Center, City University of New York Title: Reduction of Modal Logic and Realization in Justification Logic
Abstract: In this paper, we first offer basic results on modal logic: (1) a wide range of modal systems can be syntactically reduced to the modal logic K in terms of theoremhood and (2) we can restrict the forms of modal axioms without changing their deductive power in those range of modal logics. Then, based on these results, we offer a new, simple, uniform and modular proof-theoretical proof of the realization of a wide range of modal logics with possible combinations of modal axioms T, D, 4, 5 including S5 in Justification Logic. We do not use a generalization of sequent calculus such as hypersequent and nested sequent calculi. We just utilize the standard cut-free sequent calculus for K and then we show, in the realized proof in Justification Logic (corresponding to K), how to recover the realizations of the modal axioms by rewriting terms in the proof.
- - - - Wednesday, Sep 23, 2020 - - - -
- - - - Thursday, Sep 24, 2020 - - - -
Seminar in Philosophical Logic Thursday, Sep 24, 6:30 PM. (Zoom link upon request RParikh@gc.cuny.edu; will be sent automatically to seminar members) Arthur Paul Pedersen, Department of Computer Science, City College of New York, CUNY Coherent Judgment: Previsions and Forecasts
Abstract. This talk is to continue critical discussion of Persi Diaconis and Brian Skyrms' book chapter, "Judgment," from their Ten Great Ideas about Chance (Princeton University Press, 2018). Specifically, I will cover two variations on coherence advanced by de Finetti to justify his theory of personal probability, each cast in game-theoretic terms — one based on previsions, the other based on forecasting. I will show how his ideas extend both conceptually and mathematically to subsequent developments due to Savage, Anscombe & Aumann, and others. While the talk is to be self-contained, an excellent reference for broader discussion is Peter Fishburn's "Utility and Subjective Probability: Contemporary Theories," International Encyclopedia of the Social & Behavioral Sciences, 2001: 16113-16121.
- - - - Friday, Sep 25, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Sep 25, 11am
The seminar will take place virtually at 11am US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Ralf Schindler, University of Münster Martin's Maximum^++ implies the P_max axiom (*)
Forcing axioms spell out the dictum that if a statement can be forced, then it is already true. The P_max axiom (*) goes beyond that by claiming that if a statement is consistent, then it is already true. Here, the statement in question needs to come from a resticted class of statements, and 'consistent' needs to mean 'consistent in a strong sense.' It turns out that (*) is actually equivalent to a forcing axiom, and the proof is by showing that the (strong) consistency of certain theories gives rise to a corresponding notion of forcing producing a model of that theory. This is joint work with D. Asperó building upon earlier work of R. Jensen and (ultimately) Keisler's 'consistency properties'.
Next Week in Logic at CUNY:
- - - - Monday, Sep 28, 2020 - - - -
Logic and Metaphysics Workshop Date: Monday, September 29st, 4.15-6.15 (NY time)
For zoom information, email Yale Weiss at: yweiss@gradcenter.cuny.edu. Speaker: Daniel Hoek (Virginia Tech) Title: Coin flips, Spinning Tops and the Continuum Hypothesis
Abstract: By using a roulette wheel or by flipping a countable infinity of fair coins, we can randomly pick out a point on a continuum. In this talk I will show how to combine this simple observation with general facts about chance to investigate the cardinality of the continuum. In particular I will argue on this basis that the continuum hypothesis is false. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. A classic theorem from Banach and Kuratowski (1929), tells us that it follows, given the axioms of ZFC, that there are cardinalities between countable infinity and the cardinality of the continuum. (Get the paper here: https://philpapers.org/archive/HOECAT-2.pdf).
- - - - Tuesday, Sep 29, 2020 - - - -
- - - - Wednesday, Sep 30, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Sep 30, 2:00pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Abstract: The usual base theory used in reverse mathematics, RCA0RCA0, is the fragment of second-order arithmetic axiomatized by Δ01Δ10 comprehension and Σ01Σ10 induction. The weaker base theory RCA∗0RCA0∗ is obtained by replacing Σ01Σ10 induction with Δ01Δ10 induction (and adding the well-known axiom expexp in order to ensure totality of the exponential function). In first-order terms, RCA0RCA0 is conservative over IΣ1IΣ1 and RCA∗0RCA0∗ is conservative over BΣ1+expBΣ1+exp.
Some of the most interesting open problems in reverse mathematics concern the first-order strength of statements from Ramsey Theory, in particular Ramsey's Theorem for pairs and two colours. In this talk, I will discuss joint work with Kasia Kowalik, Tin Lok Wong, and Keita Yokoyama concerning the strength of Ramsey's Theorem over RCA∗0RCA0∗.
Given standard natural numbers n,k≥2n,k≥2, let RTnkRTkn stand for Ramsey's Theorem for kk-colourings of nn-tuples. We first show that assuming the failure of Σ01Σ10 induction, RTnkRTkn is equivalent to its own relativization to an arbitrary Σ01Σ10-definable cut. Using this, we give a complete axiomatization of the first-order consequences of RCA∗0+RTnkRCA0∗+RTkn for n≥3n≥3 (this turns out to be a rather peculiar fragment of PA) and obtain some nontrivial information about the first-order consequences of RT2kRTk2. Time permitting, we will also discuss the question whether our results have any relevance for the well-known open problem of characterizing the first-order consequences of RT22RT22 over the traditional base theory RCA0RCA0.
In the first part of the talk, we concentrated on Ramsey's Theorem for nn-tuples where n≥3n≥3. In this second part, the focus will be on RT22RT22.
The New York City Category Theory Seminar Date and Time: Wednesday September 30, 2020, 7:00 - 8:30 PM., on Zoom. Zoom information will be posted on the web page on the day of the talk http://www.sci.brooklyn.cuny.edu/~noson/CTseminar.html
Speaker: David Ellerman, University of Ljubljana. Title: The Logical Theory of Canonical Maps: The Elements & Distinctions Analysis of the Morphisms, Duality, Canonicity, and Universal Constructions in Sets.
Abstract: Category theory gives a mathematical characterization of naturality but not of canonicity. The purpose of this paper is to develop the logical theory of canonical maps based on the broader demonstration that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, canonicity, and universal constructions in Sets, the category of sets and functions. The analysis extends directly to other Sets-based concrete categories (groups, rings, vector spaces, etc.). Elements and distinctions are the building blocks of the two dual logics, the Boolean logic of subsets and the logic of partitions. The partial orders (inclusion and refinement) in the lattices for the dual logics define morphisms. The thesis is that the maps that are canonical in Sets are the ones that are defined (given the data of the situation) by these two logical partial orders and by the compositions of those maps. Paper: Available here http://www.sci.brooklyn.cuny.edu/~noson/Ellerman2020.pdf
- - - - Thursday, Oct 1, 2020 - - - -
- - - - Friday, Oct 2, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Oct 2, 3pm
The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
David Aspero, University of East Anglia
TBA
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
This Week in Logic at CUNY
This Week in Logic at CUNY
9/20/2020 21:54:11
This Week in Logic at CUNY:
- - - - Monday, Sep 21, 2020 - - - -
Logic and Metaphysics Workshop Date: Monday, September 21st, 4.15-6.15 (NY time)
For zoom information, email Yale Weiss at: yweiss@gradcenter.cuny.edu. Speaker: Yale Weiss (CUNY) Title: Arithmetical Semantics for Non-Classical Logic
Abstract: I consider logics which can be characterized exactly in the lattice of the positive integers ordered by division. I show that various (fragments of) relevant logics and intuitionistic logic are sound and complete with respect to this structure taken as a frame; different logics are characterized in it by imposing different conditions on valuations. This presentation will both cover and extend previous/forthcoming work of mine on the subject.
- - - - Tuesday, Sep 22, 2020 - - - -
- - - - Wednesday, Sep 23, 2020 - - - -
- - - - Thursday, Sep 24, 2020 - - - -
Seminar in Philosophical Logic Thursday, Sep 24, 6:30 PM. (Zoom link upon request RParikh@gc.cuny.edu; will be sent automatically to seminar members) Arthur Paul Pedersen, Department of Computer Science, City College of New York, CUNY Coherent Judgment: Previsions and Forecasts
Abstract. This talk is to continue critical discussion of Persi Diaconis and Brian Skyrms' book chapter, "Judgment," from their Ten Great Ideas about Chance (Princeton University Press, 2018). Specifically, I will cover two variations on coherence advanced by de Finetti to justify his theory of personal probability, each cast in game-theoretic terms — one based on previsions, the other based on forecasting. I will show how his ideas extend both conceptually and mathematically to subsequent developments due to Savage, Anscombe & Aumann, and others. While the talk is to be self-contained, an excellent reference for broader discussion is Peter Fishburn's "Utility and Subjective Probability: Contemporary Theories," International Encyclopedia of the Social & Behavioral Sciences, 2001: 16113-16121.
- - - - Friday, Sep 25, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Sep 25, 11am
The seminar will take place virtually at 11am US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Ralf Schindler, University of Münster Martin's Maximum^++ implies the P_max axiom (*)
Forcing axioms spell out the dictum that if a statement can be forced, then it is already true. The P_max axiom (*) goes beyond that by claiming that if a statement is consistent, then it is already true. Here, the statement in question needs to come from a resticted class of statements, and 'consistent' needs to mean 'consistent in a strong sense.' It turns out that (*) is actually equivalent to a forcing axiom, and the proof is by showing that the (strong) consistency of certain theories gives rise to a corresponding notion of forcing producing a model of that theory. This is joint work with D. Asperó building upon earlier work of R. Jensen and (ultimately) Keisler's 'consistency properties'.
Next Week in Logic at CUNY:
- - - - Monday, Sep 28, 2020 - - - -
Logic and Metaphysics Workshop Date: Monday, September 29st, 4.15-6.15 (NY time)
For zoom information, email Yale Weiss at: yweiss@gradcenter.cuny.edu. Speaker: Daniel Hoek (Virginia Tech) Title: Coin flips, Spinning Tops and the Continuum Hypothesis
Abstract: By using a roulette wheel or by flipping a countable infinity of fair coins, we can randomly pick out a point on a continuum. In this talk I will show how to combine this simple observation with general facts about chance to investigate the cardinality of the continuum. In particular I will argue on this basis that the continuum hypothesis is false. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. A classic theorem from Banach and Kuratowski (1929), tells us that it follows, given the axioms of ZFC, that there are cardinalities between countable infinity and the cardinality of the continuum. (Get the paper here: https://philpapers.org/archive/HOECAT-2.pdf).
- - - - Tuesday, Sep 29, 2020 - - - -
- - - - Wednesday, Sep 30, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Sep 30, 2:00pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Abstract: The usual base theory used in reverse mathematics, RCA0RCA0, is the fragment of second-order arithmetic axiomatized by Δ01Δ10 comprehension and Σ01Σ10 induction. The weaker base theory RCA∗0RCA0∗ is obtained by replacing Σ01Σ10 induction with Δ01Δ10 induction (and adding the well-known axiom expexp in order to ensure totality of the exponential function). In first-order terms, RCA0RCA0 is conservative over IΣ1IΣ1 and RCA∗0RCA0∗ is conservative over BΣ1+expBΣ1+exp.
Some of the most interesting open problems in reverse mathematics concern the first-order strength of statements from Ramsey Theory, in particular Ramsey's Theorem for pairs and two colours. In this talk, I will discuss joint work with Kasia Kowalik, Tin Lok Wong, and Keita Yokoyama concerning the strength of Ramsey's Theorem over RCA∗0RCA0∗.
Given standard natural numbers n,k≥2n,k≥2, let RTnkRTkn stand for Ramsey's Theorem for kk-colourings of nn-tuples. We first show that assuming the failure of Σ01Σ10 induction, RTnkRTkn is equivalent to its own relativization to an arbitrary Σ01Σ10-definable cut. Using this, we give a complete axiomatization of the first-order consequences of RCA∗0+RTnkRCA0∗+RTkn for n≥3n≥3 (this turns out to be a rather peculiar fragment of PA) and obtain some nontrivial information about the first-order consequences of RT2kRTk2. Time permitting, we will also discuss the question whether our results have any relevance for the well-known open problem of characterizing the first-order consequences of RT22RT22 over the traditional base theory RCA0RCA0.
In the first part of the talk, we concentrated on Ramsey's Theorem for nn-tuples where n≥3n≥3. In this second part, the focus will be on RT22RT22.
The New York City Category Theory Seminar Date and Time: Wednesday September 30, 2020, 7:00 - 8:30 PM., on Zoom. Zoom information will be posted on the web page on the day of the talk http://www.sci.brooklyn.cuny.edu/~noson/CTseminar.html
Speaker: David Ellerman, University of Ljubljana. Title: The Logical Theory of Canonical Maps: The Elements & Distinctions Analysis of the Morphisms, Duality, Canonicity, and Universal Constructions in Sets.
Abstract: Category theory gives a mathematical characterization of naturality but not of canonicity. The purpose of this paper is to develop the logical theory of canonical maps based on the broader demonstration that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, canonicity, and universal constructions in Sets, the category of sets and functions. The analysis extends directly to other Sets-based concrete categories (groups, rings, vector spaces, etc.). Elements and distinctions are the building blocks of the two dual logics, the Boolean logic of subsets and the logic of partitions. The partial orders (inclusion and refinement) in the lattices for the dual logics define morphisms. The thesis is that the maps that are canonical in Sets are the ones that are defined (given the data of the situation) by these two logical partial orders and by the compositions of those maps. Paper: Available here http://www.sci.brooklyn.cuny.edu/~noson/Ellerman2020.pdf
- - - - Thursday, Oct 1, 2020 - - - -
- - - - Friday, Oct 2, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Oct 2, 3pm
The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
David Aspero, University of East Anglia
TBA
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Wednesday seminar
Prague Set Theory Seminar
9/20/2020 10:49:20
Dear all,
Because of the current COVID-19 epidemic related restrictions there will
be no seminar next week, Wednesday September 23 (students are now
officially not allowed to participate seminars).
As for the following weeks, we will see how he situation develops.
Best,
David
Roman Kossak: Truth, Resplendence, and Directed Graphs with Local Finite Height
Boise Logic and Set Theory Seminar
9/17/2020
[Email the organizer scoskey@boisestate.edu for Zoom meeting number]
Speaker: Roman Kossak (CUNY)
Title: Truth, Resplendence, and Directed Graphs with Local Finite Height
Abstract: Under certain assumptions, a nonstandard model of arithmetic admits an assignment of truth values for all of its sentences, standard and nonstandard. This important result in the model theory of arithmetic was proved in 1981 by Kotlarski, Krajewski and Lachlan, with a proof employing a ``rather exotic proof-theoretic technology." In 2009, Enayat and Viser gave a much more accessible model-theoretic proof. In 2018, Schmerl isolated the graph-theoretic component of the Enayat-Visser proof, by showing that certain infinite graphs have kernels, from which the theorem can be obtained as a straightforward corollary. This story is an excellent example of how mathematics gets simplified. I will explain all basic concepts and I will outline the proof of Shmerl's result.
Schmerl's paper is at: arXiv:1807.11832
Tagged: Roman Kossak
Logic Seminar 16 Sept 2020 17:00 hrs at NUS by Ye Jinhe (Notre Dame)
NUS Logic Seminar
9/15/2020 4:23:06
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 16 September 2020, 17:00 hrs
Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Speaker: Ye Jinhe
Title: The etale open topology
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: For any field K, we introduce natural topologies on K-points of
varieties over K, which is defined to be the weakest topology such that etale
morphisms are open. This topology turns out to be natural in a lot of settings.
For example, when K is algebraically closed, it is easy to see that we have
the Zariski topology and it picks up the valuation topology in many Henselian
valued fields. Moreover, many topological properties correspond to the algebraic
properties of the field. As an application, we will show large stable fields
are separably closed, a special case of the stable fields conjecture.
This is joint work with Will Johnson, Chieu-Minh Tran and Erik Walsberg.
This Week in Logic at CUNY
This Week in Logic at CUNY
9/13/2020 22:31:31
This Week in Logic at CUNY:
- - - - Monday, Sep 14, 2020 - - - -
Logic and Metaphysics Workshop Date: Monday, September 14th, 4.15-6.15 For zoom information, email Yale Weiss at: yweiss@gradcenter.cuny.edu. Speaker: Chris Scambler (NYU) Title: Cantor’s Theorem, Modalized
Abstract: I will present a modal axiom system for set theory that (I claim) reconciles mathematics after Cantor with the idea there is only one size of infinity. I’ll begin with some philosophical background on Cantor’s proof and its relation to Russell’s paradox. I’ll then show how techniques developed to treat Russell’s paradox in modal set theory can be generalized to produce set theories consistent with the idea that there’s only one size of infinity.
- - - - Tuesday, Sep 15, 2020 - - - -
Computational Logic Seminar Fall 2020, on-line meetings Please send me a request for a link to this talk - Sergei Artemov (sartemov@gc.cuny.edu) Time 2:00 - 4:00 PM Tuesday September 15, 2020 Speaker: Sergei Artemov, Graduate Center, City University of New York Title: On Constructive Epistemic Logic
Abstract: A joint paper: S.Artemov and T.Protopopescu, Intuitionistic Epistemic Logic, The Review of Symbolic Logic 9(2):266-298, 2016, opened the door to a new avenue of active research in constructive epistemic logic. We will present the basics and comment on the current state of these studies.
- - - - Wednesday, Sep 16, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Sep 16, 5:00pm
The seminar will take place virtually at 5pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Sam Coskey, Boise State University Classification of countable models of ZFC
In 2009 Roman Kossak and I showed that the classification of countable models of PA is Borel complete, which means it is as complex as possible. The proof is a straightforward application of Gaifman’s canonical I-models. In 2017 Sam Dworetzky, John Clemens, and I showed that the argument may also be used to show the classification of countable models of ZFC is Borel complete too. In this talk I'll outline the original argument for models of PA, the adaptation for models of ZFC, and briefly consider several subclasses of countable models of ZFC.
The New York City Category Theory Seminar Date and Time: Wednesday September 16, 2020, 7:00 - 8:30 PM., on Zoom. Zoom information will be posted on the web page on the day of the talk http://www.sci.brooklyn.cuny.edu/~noson/CTseminar.html
Speaker: Rick Jardine, University of Western Ontario.
Title: Posets, metric spaces, and topological data analysis.
Abstract: Traditional TDA is the analysis of homotopy invariants of systems of spaces V(X) that arise from finite metric spaces X, via distance measures. These spaces can be expressed in terms of posets, which are barycentric subdivisions of the usual Vietoris-Rips complexes V(X). The proofs of stability theorems in TDA are sharpened considerably by direct use of poset techniques.
Expanding the domain of definition to extended pseudo metric spaces enables the construction of a realization functor on diagrams of spaces, which has a right adjoint Y |--> S(Y), called the singular functor. The realization of the Vietoris-Rips system V(X) for an ep-metric space X is the space itself. The counit of the adjunction defines a map \eta: V(X) --> S(X), which is a sectionwise weak equivalence - the proof uses simplicial approximation techniques.
This is the context for the Healy-McInnes UMAP construction, which will be discussed if time permits. UMAP is non-traditional: clusters for UMAP are defined by paths through sequences of neighbour pairs, which can be a highly efficient process in practice.
- - - - Thursday, Sep 17, 2020 - - - -
Zoom seminar in Philosophical Logic Contact Rohit Parikh (rparikh@gc.cuny.edu) for zoom link.
Thursday September 17 at 6:30 PM Larry Moss of Indiana University will speak about Judgment from
the recent book by Diaconis and Skyrms
- - - - Friday, Sep 18, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Sep 18, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Arthur Apter, CUNY UA and the Number of Normal Measures over ℵω+1ℵω+1 The Ultrapower Axiom UA, introduced by Goldberg and Woodin, is known to have many striking consequences. In particular, Goldberg has shown that assuming UA, the Mitchell ordering of normal measures over a measurable cardinal is linear. I will discuss how this result may be used to construct choiceless models of ZF in which the number of normal measures at successors of singular cardinals can be precisely controlled.
Next Week in Logic at CUNY:
- - - - Monday, Sep 21, 2020 - - - -
- - - - Tuesday, Sep 22, 2020 - - - -
- - - - Wednesday, Sep 23, 2020 - - - -
- - - - Thursday, Sep 24, 2020 - - - -
- - - - Friday, Sep 25, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Sep 25, 11am
The seminar will take place virtually at 11am US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Ralf Schindler, University of Münster Martin's Maximum^++ implies the P_max axiom (*)
Forcing axioms spell out the dictum that if a statement can be forced, then it is already true. The P_max axiom (*) goes beyond that by claiming that if a statement is consistent, then it is already true. Here, the statement in question needs to come from a resticted class of statements, and 'consistent' needs to mean 'consistent in a strong sense.' It turns out that (*) is actually equivalent to a forcing axiom, and the proof is by showing that the (strong) consistency of certain theories gives rise to a corresponding notion of forcing producing a model of that theory. This is joint work with D. Asperó building upon earlier work of R. Jensen and (ultimately) Keisler's 'consistency properties'.
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
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Wednesday seminar
Prague Set Theory Seminar
9/13/2020 8:47:47
Dear all,
Mirna Džamonja (IHPST CNRS-Université Panthéon-Sorbonne, Paris) will be
visiting the Institute of Mathematics CAS during the upcoming week. She
will give talks both at the Set Theory and Analysis seminar on Tuesday
September 15th at 10 AM and the at the Wednesday seminar. The
announcement for the Tuesday seminar is here:
https://calendar.math.cas.cz/set-theory-and-analysis-actual
The Seminar on Reckoning meets on Wednesday September 16th at 11:00 in
the Institute of Mathematics CAS, Zitna 25.
!!!
In order to be able to comply with the current 2 meters separation rule
the seminar changes location next week. We will meet in the blue lecture
room on the ground floor of the rear building.
!!!
Program: Mirna Džamonja -- On wide Aronszajn trees
Aronszajn trees are a staple of set theory, but there are applications
where the requirement of all levels being countable is of no importance.
This is the case in set-theoretic model theory, where trees of height
and size ω1 but with no uncountable branches play an important role by
being clocks of Ehrenfeucht--Fraïssé games that measure similarity of
model of size ℵ1. We call such trees wide Aronszajn. In this context one
can also compare trees T and T’ by saying that T weakly embeds into T’
if there is a function f that map T into T’ while preserving the strict
order <_T. This order translates into the comparison of winning
strategies for the isomorphism player, where any winning strategy for T’
translates into a winning strategy for T’. Hence it is natural to ask if
there is a largest such tree, or as we would say, a universal tree for
the class of wood Aronszajn trees with weak embeddings. It was known
that there is no such a tree under CH, but in 1994 Mekler and Väänanen
conjectured that there would be under MA(ω1).
In our upcoming JSL paper with Saharon Shelah we prove that this is not
the case: under MA(ω1) there is no universal wide Aronszajn tree.
The talk will discuss that paper. The paper is available on the arxiv
and on line at JSL in the preproof version DOI: 10.1017/jsl.2020.42
Best,
David
Wednesday seminar
Prague Set Theory Seminar
9/13/2020 8:47:47
Dear all,
Mirna Džamonja (IHPST CNRS-Université Panthéon-Sorbonne, Paris) will be
visiting the Institute of Mathematics CAS during the upcoming week. She
will give talks both at the Set Theory and Analysis seminar on Tuesday
September 15th at 10 AM and the at the Wednesday seminar. The
announcement for the Tuesday seminar is here:
https://calendar.math.cas.cz/set-theory-and-analysis-actual
The Seminar on Reckoning meets on Wednesday September 16th at 11:00 in
the Institute of Mathematics CAS, Zitna 25.
!!!
In order to be able to comply with the current 2 meters separation rule
the seminar changes location next week. We will meet in the blue lecture
room on the ground floor of the rear building.
!!!
Program: Mirna Džamonja -- On wide Aronszajn trees
Aronszajn trees are a staple of set theory, but there are applications
where the requirement of all levels being countable is of no importance.
This is the case in set-theoretic model theory, where trees of height
and size ω1 but with no uncountable branches play an important role by
being clocks of Ehrenfeucht--Fraïssé games that measure similarity of
model of size ℵ1. We call such trees wide Aronszajn. In this context one
can also compare trees T and T’ by saying that T weakly embeds into T’
if there is a function f that map T into T’ while preserving the strict
order <_T. This order translates into the comparison of winning
strategies for the isomorphism player, where any winning strategy for T’
translates into a winning strategy for T’. Hence it is natural to ask if
there is a largest such tree, or as we would say, a universal tree for
the class of wood Aronszajn trees with weak embeddings. It was known
that there is no such a tree under CH, but in 1994 Mekler and Väänanen
conjectured that there would be under MA(ω1).
In our upcoming JSL paper with Saharon Shelah we prove that this is not
the case: under MA(ω1) there is no universal wide Aronszajn tree.
The talk will discuss that paper. The paper is available on the arxiv
and on line at JSL in the preproof version DOI: 10.1017/jsl.2020.42
Best,
David
Wednesday seminar
Prague Set Theory Seminar
9/7/2020 4:39:58
Dear all,
The seminar meets on Wednesday September 9th at 11:00 in the Institute
of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
The program is not yet determined, walk-in speakers are welcome.
Otherwise we have the usual backup option of me talking about something..
Best,
David
Kyoto University Research Institute for Mathematical Sciences
Set Theory Workshop, November 16-20, 2020
Conference
9/7/2020
Kyoto University Research Institute for Mathematical Sciences
Set Theory Workshop 2020
Set Theory: Reals and Topology
November 16-20, 2020
http://strims2020.sa-suke.com
Call for lectures and participation
Due to the COVID-19 pandemic, the workshop will take place online. This is the first online version of this workshop.
Every year, set theory researchers from Japan and abroad gather at the RIMS (Research Institute for Mathematical Sciences) of Kyoto University and hold an international workshop that brings together both expert and young researchers of set theory. As indicated in the title “Set Theory: Reals and Topology”, the main topic this year is about the developments of set theory and its interaction with combinatorics of the reals and topology.
We encourage both young researchers and experts, from Japan and abroad, to contribute with lectures in any topic of Set Theory (not necessarily in the main topic). We expect participation (even without lecture) of many researchers in the area and graduate students. Registration is required for participation (see details on the webpage).
Registration deadlines:
For contributed lectures: October 1st, 2020.
For participation (without lecture): October 15th, 2020.
Minicourse Speakers
Osvaldo Guzmán (Universidad Nacional Autónoma de México)
Ashutosh Kumar (Indian Institute of Technology Kampur)
Invited Speakers
Martin Goldstern (TU Wien)
Ulises Ariet Ramos-García (Universidad Nacional Autónoma de México)
Organizer:
Diego A. Mejía (Shizuoka University)
Scientific Committee:
Teruyuki Yorioka (Shizuoka University)
Dilip Raghavan (National University of Singapore)
Tagged: Osvaldo Guzmán, Ashutosh Kumar, Martin Goldstern, Ulises Ariet Ramos-García, Diego A. Mejía
This Week in Logic at CUNY
This Week in Logic at CUNY
9/6/2020 20:28:03
This Week in Logic at CUNY:
- - - - Monday, Sep 7, 2020 - - - -
- - - - Tuesday, Sep 8, 2020 - - - -
************************ Computational Logic Seminar Fall 2020, on-line meetings Time 2:00 - 4:00 PM Tuesday, September 8, 2020 Please send a request for a link to this talk (unless you are registered of have already sent me a request for the whole semester): sartemov@gc.cuny.edu Speaker: Melvin Fitting, Graduate Center, City University of New York Title: About `Binding Modalities'
Abstract: In classical logic the addition of quantifiers to propositional logic is essentially unique, with some minor variations of course. In modal logic things are not so monolithic. One can quantify over things or over intensions; domains can be the same from possible world to possible world, or shrink, or grow, or follow no pattern, as one moves from a possible world to an accessible one. In 1963 Kripke showed that shrinking or growing domains related to validity of the Barcan and the converse Barcan formulas, but this was a semantic result. Proof theory is trickier. Nested sequents are well behaved, but axiom systems can be unruly. A direct combination of propositional modal axioms and rules with standard quantificational axioms and rules simply proves the converse Barcan formula. It's not easy to get rid of it. Kripke showed how one could do so, but he needed to use a less common axiomatization of the quantifiers. It works, but one has the impression of having a formal proof system with road blocks placed carefully to prevent proofs from veering into the ditch. Some 40 or more years later, justification logic was created by Artemov, and now there are justification systems that correspond to infinitely many different modal logics. The first justification logic was called LP, for logic of proofs. It is related to propositional S4. LP was extended to a quantified version by Artemov and Yavorskaya, with a possible world semantics supplied by Fitting. Subsequently Artemov and Yavorskaya transferred their ideas, concerning what they called binding modalities, back from quantified LP to quantified S4 itself. In the present work we carry their ideas on further to the basic normal modal logic, K, which is not as well-behaved as S4 on these matters. It turns out that this provides a natural intuition for Kripke's non-standard axiomatization from those many years ago. It also relates quite plausibly to the distinction between de re and de dicto. But now the main work is done through a generalization of the modal operator, instead of through a restriction on allowed quantifier axiomatizations.
- - - - Wednesday, Sep 9, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Sep 9, 3:00pm
The seminar will take place virtually at 3pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Saeideh Bahrami, Institute for Research in Fundamental Sciences, Tehran Fixed Points of Initial Self-Embeddings of Models of Arithmetic In 1973, Harvey Friedman proved his striking result on initial self-embeddings of countable nonstandard models of set theory and Peano arithmetic. In this talk, I will discuss my joint work with Ali Enayat focused on the fixed point set of initial self-embeddings of countable nonstandard models of arithmetic. Especially, I will survey the proof of some generalizations of well-known results on the fixed point set of automorphisms of countable recursively saturated models of PAPA, to results about the fixed point set of initial self-embeddings of countable nonstandard models of IΣ1IΣ1.
- - - - Thursday, Sep 10, 2020 - - - -
- - - - Friday, Sep 11, 2020 - - - -
Next Week in Logic at CUNY:
- - - - Monday, Sep 14, 2020 - - - -
Logic and Metaphysics Workshop Date: Monday, September 14th, 4.15-6.15 For zoom information, email Yale Weiss at: yweiss@gradcenter.cuny.edu. Speaker: Chris Scambler (NYU) Title: Cantor’s Theorem, Modalized
Abstract: I will present a modal axiom system for set theory that (I claim) reconciles mathematics after Cantor with the idea there is only one size of infinity. I’ll begin with some philosophical background on Cantor’s proof and its relation to Russell’s paradox. I’ll then show how techniques developed to treat Russell’s paradox in modal set theory can be generalized to produce set theories consistent with the idea that there’s only one size of infinity.
- - - - Tuesday, Sep 15, 2020 - - - -
- - - - Wednesday, Sep 16, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Sep 16, 5:00pm
The seminar will take place virtually at 5pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Sam Coskey, Boise State University TBA
- - - - Thursday, Sep 17, 2020 - - - -
- - - - Friday, Sep 18, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Sep 18, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Arthur Apter, CUNY UA and the Number of Normal Measures over ℵω+1ℵω+1 The Ultrapower Axiom UA, introduced by Goldberg and Woodin, is known to have many striking consequences. In particular, Goldberg has shown that assuming UA, the Mitchell ordering of normal measures over a measurable cardinal is linear. I will discuss how this result may be used to construct choiceless models of ZF in which the number of normal measures at successors of singular cardinals can be precisely controlled.
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
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To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Logic Seminar 9 Sept 2020 17:00 hrs at NUS by Ming Xiao
NUS Logic Seminar
8/31/2020 21:45:54
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 9 September 2020, 17:00 hrs
Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Speaker: Ming Xiao
Title: A Borel Chain Condition of T(X)
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
In 1948, Horn and Tarski conjectured whether the sigma-finite chain
condition and sigma-bounded chain condition are equivalent. The first
counterexample was given by Thummel in 2012 and then a Borel
counterexample was given by Todorvevic in 2014. Both examples belong to a
class of poset called "Todorvevic ordering" T(X) over topological spaces
X. In this talk, I will illustrate a satisfactory condition for a
topological space X making the corresponding poset T(X) fail to have a
countable Borel partition witnessing the sigma-finite chain condition,
although it may still be witnessed by non-Borel partitions.
The content of this talk is going to be the same as the one I gave in a
seminar at the Chinese Academy of Sciences last year and is also a part of
my Ph.D. dissertation.
This Week in Logic
This Week in Logic at CUNY
8/30/2020 22:30:02
Hi everyone,
Classes started at CUNY last week, and regular mailings of this newsletter will continue through the Fall semester. Please let me know if you have logic-related events at CUNY or elsewhere that you would like to include.
The seminar will take place virtually at 3pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
September 2 Petr Glivický, Universität Salzburg The ωω-iterated nonstandard extension of NN and Ramsey combinatorics
In the theory of nonstandard methods (traditionally known as nonstandard analysis), each mathematical object (a set) xx has a uniquely determined so called nonstandard extension ∗x∗x. In general, ∗x⊋{∗y;y∈x}∗x⊋{∗y;y∈x} - that is, besides the original 'standard' elements ∗y∗y for y∈xy∈x, the set ∗x∗x contains some new 'nonstandard' elements.
For instance, some of the nonstandard elements of ∗R∗R can be interpreted as infinitesimals (there is ε∈∗Rε∈∗R such that 0<ε<1/n0<ε<1/n for all n∈Nn∈N) allowing for nonstandard analysis to be developed in ∗R∗R, while ∗N∗N turns out to be an (at least ℵ1ℵ1-saturated) nonstandard elementary extension of NN (in the language of arithmetic).
While the whole nonstandard real analysis is most naturally developed in ∗R∗R (with just a few advanced topics where using the second extension ∗∗R∗∗R is convenient, though far from necessary), recent successful applications of nonstandard methods in combinatorics on NN have utilized also higher order extensions (n)∗N=∗∗∗⋯∗N(n)∗N=∗∗∗⋯∗N with the chain ∗∗∗⋯∗∗∗∗⋯∗ of length n>2n>2.
In this talk we are going to study the structure of the ωω-iterated nonstandard extension ⋅N=⋃n∈ω(n)∗N⋅N=⋃n∈ω(n)∗N of NN and show how the obtained results shed new light on the complexities of Ramsey combinatorics on NN and allow us to drastically simplify proofs of many advanced Ramsey type theorems such as Hindmann's or Milliken's and Taylor's.
- - - - Thursday, Sep 03, 2020 - - - -
Seminar in philosophical logic
Thursday, Sep 3, 6:30pm
Rohit Parikh, City University of New York
On September 3 I will give a talk in the Zoom seminar in philosophical logic which takes place on Thursdays at 6:30 PM.
I will speak about the Sorites paradox and vagueness, relying on previous work by Michael Dummett, Kit Fine, Lotfi Zadeh and myself. I hope you will find it enjoyable.
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Mirna Džamonja, IHPST, CNRS-Université Panthéon-Sorbonne Paris, France On logics that make a bridge from the Discrete to the Continuous We study logics which model the passage between an infinite sequence of finite models to an uncountable limiting object, such as is the case in the context of graphons. Of particular interest is the connection between the countable and the uncountable object that one obtains as the union versus the combinatorial limit of the same sequence.
Next Week in Logic at CUNY:
- - - - Monday, Sep 7, 2020 - - - -
- - - - Tuesday, Sep 8, 2020 - - - -
- - - - Wednesday, Sep 9, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Sep 9, 3:00pm
The seminar will take place virtually at 3pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Saeideh Bahrami, Institute for Research in Fundamental Sciences, Tehran Fixed Points of Initial Self-Embeddings of Models of Arithmetic In 1973, Harvey Friedman proved his striking result on initial self-embeddings of countable nonstandard models of set theory and Peano arithmetic. In this talk, I will discuss my joint work with Ali Enayat focused on the fixed point set of initial self-embeddings of countable nonstandard models of arithmetic. Especially, I will survey the proof of some generalizations of well-known results on the fixed point set of automorphisms of countable recursively saturated models of PAPA, to results about the fixed point set of initial self-embeddings of countable nonstandard models of IΣ1IΣ1.
- - - - Thursday, Sep 10, 2020 - - - -
- - - - Friday, Sep 11, 2020 - - - -
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Wednesday seminar
Prague Set Theory Seminar
8/27/2020 6:04:35
Dear all,
The seminar meets on Wednesday September 2nd at 11:00 in the Institute
of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: David Uhrik -- Partition relations on omega_2
I will present Baumgartner's proof (paper attached) of the consistency
of the partition relation omega_2 --> (omega_2, omega : 2)^2 without
using large cardinals and talk about related results.
Best,
David
Logic Seminar 26 Aug 2020 17:00 hrs at NUS
NUS Logic Seminar
8/23/2020 22:32:40
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 26 August 2020, 17:00 hrs
Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Speaker: Gordon Hoi
Title: A Faster Exact Algorithm to Count X3SAT Solutions
Abstract: The Exact Satisfiability problem, XSAT, is defined as the
problem of finding a satisfying assignment to a formula in CNF such
that there is exactly one literal in each clause assigned to be 1 and
the other literals in the same clause are set to 0. If we restrict
the length of each clause to be at most 3 literals,
then it is known as the X3SAT problem. In this paper, we consider
the problem of counting the number of satisfying assignments to
the X3SAT problem, which is also known as #X3SAT.
The current state of the art exact algorithm to solve #X3SAT
is given by Dahlloef, Jonsson and Beigel and runs in
O(1.1487^n), where n is the number of variables in
the formula. In this paper, we propose an exact algorithm
for the #X3SAT problem that runs in O(1.1120^n) with very few
branching cases to consider, by using a result from Monien
and Preis to give us a bisection width for graphs with at
most degree 3.
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Logic Seminar Login Details
NUS Logic Seminar
8/19/2020 4:50:02
Hello,
Here the details of the logic seminar Zoom logins for this semester
for those who forgot. The seminar starts in 10 minutes. Cristian
Calude will give the talk. It is 17:00 hrs Singapore time.
Best regards, Frank
Join Zoom Meeting
https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Logic Seminar 19 August 2020 17:00 hrs at NUS (Zoom)
NUS Logic Seminar
8/16/2020 23:32:22
Hello, for the logic seminar, there might be some error in the Zoom details.
The correct ones are as follows:
Join Zoom Meeting
https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Wednesday, 17:00 hrs Singapore time (= 21:00 hrs New Zealand time,
18:00 hrs Japan time and 11:00 hrs German time), this week.
Best regards, Frank
Wednesday seminar
Prague Set Theory Seminar
8/14/2020 5:27:34
Dear all,
There is no seminar next week, Wednesday August 19 due to
vacations/holidays.
The seminar the week after that is uncertain (no announcement = no
seminar). The seminar should meet again in September.
Best,
David
Logic Seminar 19 August 2020 17:00 hrs at NUS (Zoom)
NUS Logic Seminar
8/14/2020 3:59:39
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 19 August 2020, 17:00 hrs
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Cristian Calude
Title: A New Quantum Random Number Generator Certified by Value Indefiniteness
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
We present a new ternary QRNG based on measuring located value indefinite
observables with probabilities 1/4,1/2,1/4 and prove that every
sequence generated is maximally unpredictable, 3-bi-immune (a stronger
form of bi-immunity), and its prefixes are Borel normal. The ternary
quantum random digits produced by the QRNG are algorithmically transformed
into quantum random bits using an alphabetic morphism which preserves all
the above properties.
Zoom: 968 6020 1432. Password: "Is P=NP?"
Link: https://nus-sg.zoom.us/j/94862783492?pwd=eUo0aUdialQrZkt1dDlFNnB4QmtDdz09
Logic Seminar Wed 12 August 2020 17:00 hrs at NUS
NUS Logic Seminar
8/10/2020 18:07:22
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 12 August 2020, 17:00 hrs
Zoom: https://nus-sg.zoom.us/j/94862783492?pwd=eUo0aUdialQrZkt1dDlFNnB4QmtDdz09
Meeting ID: 948 6278 3492
Password: 811969
Speaker: Frank Stephan
Title: Initial Segment Complexity for Measures - Results and Open Problems
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: The initial segment complexity of a measure mu at n is given by the
sum over all mu(x)*C(x) with x of length n for the plain complexity C and
similarly for the prefix-free Kolmogorov complexity. This talk gives the
basic relations between initial segment complexity and randomness notions
and lists out various open questions which arise from this work. The same
work was presented at the American Institute of Mathematics in this week's
programme on Algorithmic Randomness.
Wednesday seminar
Prague Set Theory Seminar
8/7/2020 11:08:11
Dear all,
The seminar meets on Wednesday August 12th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: David Chodounsky -- Big Ramsey degrees of hypergraphs (continued)
I will continue the talk on big Ramsey degrees of hypergraphs, this time
I plan to give more details of the finiteness proof for the 3-uniform case.
The preprint is now online: https://arxiv.org/abs/2008.00268
Best,
David
Wednesday seminar
Prague Set Theory Seminar
7/31/2020 6:29:06
Dear all,
There is no seminar next week. You might be interested in participating
the Midsummer Combinatorial Workshop instead.
https://kam.mff.cuni.cz/workshops/mcw/
The seminar will meet again on Wednesday August 12th.
Best,
David
This Week in Logic at CUNY
This Week in Logic at CUNY
7/26/2020 22:59:40
This Week in Logic at CUNY:
- - - - Monday, Jul 27, 2020 - - - -
- - - - Tuesday, Jul 28, 2020 - - - -
- - - - Wednesday, Jul 29, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, July 29, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Kameryn Williams, University of Hawai‘i at Mānoa End-extensions of models of set theory and the Σ1Σ1 universal finite sequence
Recall that if M⊆NM⊆N are models of set theory then NN end-extends MM if NN does not have new elements for sets in MM. In this talk I will discuss a Σ1Σ1-definable finite sequence which is universal for end extensions in the following sense. Consider a computably axiomatizable extension ¯¯¯¯¯¯¯ZFZF¯ of ZFZF. There is a Σ1Σ1-definable finite sequencea0,a1,…,ana0,a1,…,anwith the following properties.
* ZFZF proves that the sequence is finite. * In any transitive model of ¯¯¯¯¯¯¯ZFZF¯ the sequence is empty. * If MM is a countable model of ¯¯¯¯¯¯¯ZFZF¯ in which the sequence is ss and t∈Mt∈M is a finite sequence extending ss then there is an end-extension N⊨¯¯¯¯¯¯¯ZFN⊨ZF¯ of MM in which the sequence is exactly tt. * Indeed, for the previous statements it suffices that M⊨ZFM⊨ZF and end-extends a submodel W⊨¯¯¯¯¯¯¯ZFW⊨ZF¯ of height at least (ωL1)M(ω1L)M.
This universal finite sequence can be used to determine the modal validities of end-extensional set-theoretic potentialism, namely to be exactly the modal theory S4S4. The sequence can also be used to show that every countable model of set theory extends to a model satisfying the end-extensional maximality principle, asserting that any possibly necessary sentence is already true.
This talk is about joint work with Joel David Hamkins. The Σ1Σ1 universal finite sequence is a sister to the Σ2Σ2 universal finite sequence for rank-extensions of Hamkins and Woodin, and both are cousins of Woodin's universal algorithm for arithmetic.
- - - - Thursday, Jul 30, 2020 - - - -
- - - - Friday, Jul 31, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, July 31, 12pm
The seminar will take place virtually at 12pm US Eastern Standard Time. Please email Victoria Gitman for meeting id.
Corey Switzer, CUNY Dissertation defense: Alternative Cichoń diagrams and forcing axioms compatible with CH This dissertation surveys several topics in the general areas of iterated forcing, infinite combinatorics and set theory of the reals. There are two parts. In the first half I consider alternative versions of the Cichoń diagram. First I show that for a wide variety of reduction concepts there is a Cichoń diagram for effective cardinal characteristics relativized to that reduction. As an application I investigate in detail the Cichoń diagram for degrees of constructibility relative to a fixed inner model of ZFC. Then I study generalizations of cardinal characteristics to the space of functions from ωωωω to ωωωω. I prove that these cardinals can be organized into two diagrams analogous to the standard Cichoń diagram show several independence results and investigate their relation to cardinal invariants on omega. In the second half of the thesis I look at forcing axioms compatible with CH. First I consider Jensen's subcomplete and subproper forcing. I generalize these notions to larger classes which are (apparently) much more nicely behaved structurally. I prove iteration and preservation theorems for both classes and use these to produce many new models of the subcomplete forcing axiom. Finally I deal with dee-complete forcing and its associated axiom DCFA. Extending a well-known result of Shelah, I show that if a tree of height ω1ω1 with no branch can be embedded into an ω1ω1 tree, possibly with uncountable branches, then it can be specialized without adding reals. As a consequence I show that DCFA implies there are no Kurepa trees, even if CH fails.
Next Week in Logic at CUNY:
- - - - Monday, Aug 3, 2020 - - - -
- - - - Tuesday, Aug 4, 2020 - - - -
- - - - Wednesday, Aug 5, 2020 - - - -
- - - - Thursday, Aug 6, 2020 - - - -
- - - - Friday, Aug 7, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Aug 7, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman for meeting id.
Brent Cody, Virginia Commonwealth University
TBA
- - - - Other Logic News - - - -
A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website, nylogic.github.io, take a look at the following for more seminar listings:
Online seminars and talks in Logic
A list of existing seminar series with talks available online, and links to recorded talks:
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Wednesday seminar
Prague Set Theory Seminar
7/22/2020 10:21:05
Dear all,
The seminar meets on Wednesday July 29th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Egbert Thümmel -- There are no tall analytic Ramsey ideals
An ideal I on omega is said to be Ramsey if the partition relation I^+
-> (I^+)_2^2 does hold. Answering a question of Hrušák and Thümmel, we
show that there are no tall analytic Ramsey ideals. We also show that
every analytic ideal is either included in an F_sigma ideal, or it has a
restriction which is Katětov-above the ideal generated by convergent
sequences of rationals.
Best,
David
Logic summer school at Fudan University, August 10-21, 2020
Conference
7/21/2020
We are organising a logic summer school at Fudan University from Aug 10 - Aug 21. It will be delivered via Zoom meeting. In the first week, Prof. Renling Jin will talk about nonstandard analysis (please note that this part will be in Chinese). In the second week, Prof. Ralf Schindler will introduce the proof of Woodin's (∗) axiom from Martin's Maximum++. Participants are encouraged to fill a registration form, and we will send the Zoom meeting ID accordingly.
For more information, we have a webpage for the summer school: http://logic.fudan.edu.cn/event2020/summer.
The seminar will take place virtually at 8pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Tin Lok Wong, National University of Singapore Properties preserved in cofinal extensions Cofinal extensions generally preserve many more properties of a model of arithmetic than their sisters, end extensions. Exactly how much must or can they preserve? The answer is intimately related to how much arithmetic the model can do. I will survey what is known and what is not known about this question, and report on some recent work on this line.
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman for meeting id.
Andrew Brooke-Taylor, University of Leeds Measurable cardinals and limits in the category of sets An old result of Isbell characterises measurable cardinals in terms of certain canonical limits in the category of sets. After introducing this characterisation, I will talk about recent work with Adamek, Campion, Positselski and Rosicky teasing out the importance of the canonicity for this and related results. The language will be category-theoretic but the proofs will be quite hands-on combinatorial constructions with sets.
Next Week in Logic at CUNY:
- - - - Monday, Jul 27, 2020 - - - -
- - - - Tuesday, Jul 28, 2020 - - - -
- - - - Wednesday, Jul 29, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, July 29, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Kameryn Williams, University of Hawai‘i at Mānoa End-extensions of models of set theory and the Σ1Σ1 universal finite sequence
Recall that if M⊆NM⊆N are models of set theory then NN end-extends MM if NN does not have new elements for sets in MM. In this talk I will discuss a Σ1Σ1-definable finite sequence which is universal for end extensions in the following sense. Consider a computably axiomatizable extension ¯¯¯¯¯¯¯ZFZF¯ of ZFZF. There is a Σ1Σ1-definable finite sequencea0,a1,…,ana0,a1,…,anwith the following properties.
* ZFZF proves that the sequence is finite. * In any transitive model of ¯¯¯¯¯¯¯ZFZF¯ the sequence is empty. * If MM is a countable model of ¯¯¯¯¯¯¯ZFZF¯ in which the sequence is ss and t∈Mt∈M is a finite sequence extending ss then there is an end-extension N⊨¯¯¯¯¯¯¯ZFN⊨ZF¯ of MM in which the sequence is exactly tt. * Indeed, for the previous statements it suffices that M⊨ZFM⊨ZF and end-extends a submodel W⊨¯¯¯¯¯¯¯ZFW⊨ZF¯ of height at least (ωL1)M(ω1L)M.
This universal finite sequence can be used to determine the modal validities of end-extensional set-theoretic potentialism, namely to be exactly the modal theory S4S4. The sequence can also be used to show that every countable model of set theory extends to a model satisfying the end-extensional maximality principle, asserting that any possibly necessary sentence is already true.
This talk is about joint work with Joel David Hamkins. The Σ1Σ1 universal finite sequence is a sister to the Σ2Σ2 universal finite sequence for rank-extensions of Hamkins and Woodin, and both are cousins of Woodin's universal algorithm for arithmetic.
- - - - Thursday, Jul 30, 2020 - - - -
- - - - Friday, Jul 31, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, July 31, 12pm
The seminar will take place virtually at 12pm US Eastern Standard Time. Please email Victoria Gitman for meeting id.
Corey Switzer, CUNY Dissertation defense: Alternative Cichoń diagrams and forcing axioms compatible with CH This dissertation surveys several topics in the general areas of iterated forcing, infinite combinatorics and set theory of the reals. There are two parts. In the first half I consider alternative versions of the Cichoń diagram. First I show that for a wide variety of reduction concepts there is a Cichoń diagram for effective cardinal characteristics relativized to that reduction. As an application I investigate in detail the Cichoń diagram for degrees of constructibility relative to a fixed inner model of ZFC. Then I study generalizations of cardinal characteristics to the space of functions from ωωωω to ωωωω. I prove that these cardinals can be organized into two diagrams analogous to the standard Cichoń diagram show several independence results and investigate their relation to cardinal invariants on omega. In the second half of the thesis I look at forcing axioms compatible with CH. First I consider Jensen's subcomplete and subproper forcing. I generalize these notions to larger classes which are (apparently) much more nicely behaved structurally. I prove iteration and preservation theorems for both classes and use these to produce many new models of the subcomplete forcing axiom. Finally I deal with dee-complete forcing and its associated axiom DCFA. Extending a well-known result of Shelah, I show that if a tree of height ω1ω1 with no branch can be embedded into an ω1ω1 tree, possibly with uncountable branches, then it can be specialized without adding reals. As a consequence I show that DCFA implies there are no Kurepa trees, even if CH fails.
- - - - Other Logic News - - - -
A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website, nylogic.github.io, take a look at the following for more seminar listings:
Online seminars and talks in Logic
A list of existing seminar series with talks available online, and links to recorded talks:
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Wednesday seminar
Prague Set Theory Seminar
7/17/2020 5:41:13
Dear all,
The seminar meets on Wednesday July 22nd at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: David Chodounsky -- Big Ramsey degrees of hypergraphs
I will talk about recent developments concerning Big Ramsey degrees of
universal homogeneous hypergraphs. In particular, we may go through a
proof that these are finite in the 3-uniform case.
Best,
David
Wednesday seminar
Prague Set Theory Seminar
7/10/2020 10:08:15
Dear all,
The seminar meets on Wednesday July 15th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: David Uhrik will talk about the paper of Stevo Todorcevic:
Erdős–Kakutani phenomena for paths (attached).
Best,
David
This Week in Logic at CUNY
This Week in Logic at CUNY
7/6/2020 11:13:37
This Week in Logic at CUNY:
- - - - Monday, Jul 6, 2020 - - - -
- - - - Tuesday, Jul 7, 2020 - - - -
- - - - Wednesday, Jul 8, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, July 8, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Corey Switzer, CUNY Axiomatizing Kaufmann models in strong logics A Kaufmann model is an ω1ω1-like, recursively saturated, rather classless model of PA. Such models were constructed by Kaufmann under the ♢♢ assumption and then shown to exist in ZFC by Shelah using an absoluteness argument involving the logic Lω1,ω(Q)Lω1,ω(Q) where QQ is the quantifier 'there exists uncountably many…'. It remains an intriguing, if vague, open problem whether one can construct a Kaufmann model in ZFC 'by hand' i.e. without appealing to some form of absoluteness or other very non-constructive methods. In this talk I consider the related problem of axiomatizing Kaufmann models in Lω1,ω(Q)Lω1,ω(Q) and show that this is independent of ZFC. Along the way we'll see that it is also independent of ZFC whether there is an ω1ω1-preserving forcing notion adding a truth predicate to a Kaufmann model.
- - - - Thursday, Jul 9, 2020 - - - -
- - - - Friday, Jul 10, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, July 10, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman for meeting id.
Peter Holy, University of Udine Uniform large cardinal characterizations and ideals up to measurability
Many prominent large cardinal notions up to measurability can be characterized by the existence of certain ultrafilters for small models of set theory. Most prominently, this includes weakly compact, ineffable, Ramsey and completely ineffable cardinals, but there are many more, and our characterization schemes also give rise to many new natural large cardinal concepts. Moreover, these characterizations allow for the uniform definition of ideals associated to these large cardinals, which agree with the ideals from the set-theoretic literature (for example, the weakly compact, the ineffable, the Ramsey or the completely ineffable ideal) whenever such had been previously established. For many large cardinal notions, we can show that their ordering with respect to direct implication, but also with respect to consistency strength corresponds in a very canonical way to certain relations between their corresponding large cardinal ideals. This is all material from a fairly extensive joint paper with Philipp Luecke, and I will try to provide an overview as well as present some particular results from this paper.
Next Week in Logic at CUNY:
- - - - Monday, Jul 13, 2020 - - - -
- - - - Tuesday, Jul 14, 2020 - - - -
- - - - Wednesday, Jul 15, 2020 - - - -
- - - - Thursday, Jul 16, 2020 - - - -
- - - - Friday, Jul 17, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, July 17, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman for meeting id.
TBA Kaethe Minden Bard College at Simon's Rock
- - - - Other Logic News - - - -
A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website, nylogic.github.io, take a look at the following for more seminar listings:
Online seminars and talks in Logic
A list of existing seminar series with talks available online, and links to recorded talks:
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Wednesday seminar
Prague Set Theory Seminar
7/6/2020 4:37:07
Dear all,
The seminar meets on Wednesday July 8th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Jan Grebik -- Approximate measurable colorings
We prove that there is an approximate version of Konig's line coloring
theorem and show how to use it to deduce the result of Toth
https://arxiv.org/abs/1906.03137 about Schreier decorations.
Best,
David
Tagged: Jan Grebik
No seminar this week
Toronto Set Theory Seminar
7/2/2020 17:22:00
Hi everyone,
There won't be a seminar this week.
The regular seminar has concluded for this year and will pick up again in the fall. However, if someone would like to speak soon, let me know and I would be happy to organize something.
Have a good summer,
Bill
Wednesday seminar
Prague Set Theory Seminar
6/29/2020 4:40:27
Dear all,
There is no seminar this Wednesday due to vacations, next week it is
most likely going to be the same story (unless announced otherwise).
Working mathematicians can instead join e.g. the online seminars in
Jerusalem and Gainesville.
HUJI seminar
Wednesday July 1, 10:00 CEST
In the next few weeks Tzoor Plotinikov will present Neeman construction
of a model in which Aleph_{omega+1} has the tree property.
Zoom link:
https://huji.zoom.us/j/243676331?pwd=dU02bUVaNC9jRCtvc2lKbVJJZ2lFdz09
Meeting ID: 243 676 331
Password: 058372
University of Florida Logic Seminar
Tuesday June 30, 22:05 CEST
Jordi Lopez-Abad: The Banakh-Sack rank of a weakly compact set
abstract attached
Zoom link: https://ufl.zoom.us/s/7401025557
Best,
David
This Week in Logic at CUNY
This Week in Logic at CUNY
6/28/2020 19:36:06
This Week in Logic at CUNY:
- - - - Monday, Jun 29, 2020 - - - -
- - - - Tuesday, Jun 30, 2020 - - - -
- - - - Wednesday, Jul 1, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, July 1, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Zachiri McKenzie, Initial self-embeddings of models of set theory: Part II
In the 1973 paper 'Countable models of set theory', H. Friedman's investigation of embeddings between countable models of subsystems of ZF yields the following two striking results:
1. Every countable nonstandard model of PA is isomorphic to a proper initial segment of itself. 2. Every countable nonstandard model of a sufficiently strong subsystem of ZF is isomorphic to a proper initial segment that is a union of ranks of the original model.
Note that, in contrast to PA, in the context of set theory there are three alternative notions of 'initial segment': transitive subclass, transitive subclass that is closed under subsets and rank-initial segment. Paul Gorbow, in his Ph.D. thesis, systematically studies versions of H. Friedman's self-embedding that yield isomorphisms between a countable nonstandard model of set theory and a rank-initial segment of itself. In these two talks I will discuss recent joint work with Ali Enayat that investigates models of set theory that are isomorphic to a transitive subclass of itself. We call the maps witnessing these isomorphisms 'initial self-embeddings'. I will outline a proof of a refinement of H. Friedman's Theorem that guarantees the existence of initial self-embeddings for certain subsystems of ZF without the powerset axiom. I will then discuss several examples including a nonstandard model of ZFC minus the powerset axiom that admits no initial self-embedding, and models that separate the three different notions of self-embedding for models of set theory. Finally, I will discuss two interesting applications of our version of H. Freidman's Theorem. The first of these is a refinement of a result due to Quinsey that guarantees the existence of partially elementary proper transitive subclasses of non-standard models of ZF minus the powerset axiom. The second result shows that every countable model of ZF with a nonstandard natural number is isomorphic to a transitive subclass of the hereditarily countable sets of its own constructible universe.
- - - - Thursday, Jul 2, 2020 - - - -
- - - - Friday, Jul 3, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, July 3, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman for meeting id.
Vera Fischer, University of Vienna More ZFC inequalities between cardinal invariants
We will discuss some recent ZFC results concerning the generalized Baire spaces, and more specifically the generalized bounding number, relatives of the generalized almost disjointness number, as well as generalized reaping and domination.
Next Week in Logic at CUNY:
- - - - Monday, Jul 6, 2020 - - - -
- - - - Tuesday, Jul 7, 2020 - - - -
- - - - Wednesday, Jul 8, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, July 8, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Corey Switzer, CUNY Axiomatizing Kaufmann models in strong logics A Kaufmann model is an ω1ω1-like, recursively saturated, rather classless model of PA. Such models were constructed by Kaufmann under the ♢♢ assumption and then shown to exist in ZFC by Shelah using an absoluteness argument involving the logic Lω1,ω(Q)Lω1,ω(Q) where QQ is the quantifier 'there exists uncountably many…'. It remains an intriguing, if vague, open problem whether one can construct a Kaufmann model in ZFC 'by hand' i.e. without appealing to some form of absoluteness or other very non-constructive methods. In this talk I consider the related problem of axiomatizing Kaufmann models in Lω1,ω(Q)Lω1,ω(Q) and show that this is independent of ZFC. Along the way we'll see that it is also independent of ZFC whether there is an ω1ω1-preserving forcing notion adding a truth predicate to a Kaufmann model.
- - - - Thursday, Jul 9, 2020 - - - -
- - - - Friday, Jul 10, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, July 10, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman for meeting id.
Peter Holy, University of Udine TBA
- - - - Other Logic News - - - -
A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website, nylogic.github.io, take a look at the following for more seminar listings:
Online seminars and talks in Logic
A list of existing seminar series with talks available online, and links to recorded talks:
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
This Week in Logic at CUNY
This Week in Logic at CUNY
6/21/2020 22:54:01
This Week in Logic at CUNY:
- - - - Monday, Jun 22, 2020 - - - -
- - - - Tuesday, Jun 23, 2020 - - - -
- - - - Wednesday, Jun 24, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, June 24, 2:00pm
NOTE: 2:00pm START TIME
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Bartosz Wcisło, Polish Academy of Sciences Tarski boundary III
Truth theories investigate the notion of truth using axiomatic methods. To a fixed base theory (typically Peano Arithmetic PAPA) we add a unary predicate T(x)T(x) with the intended interpretation 'xx is a (code of a) true sentence.' Then we analyse how adding various possible sets of axioms for that predicate affects its behaviour.
One of the aspects which we are trying to understand is which truth-theoretic principles make the added truth predicate 'strong' in that the resulting theory is not conservative over the base theory. Ali Enayat proposed to call this demarcating line between conservative and non-conservative truth theories 'the Tarski boundary.'
Research on Tarski boundary revealed that natural truth theoretic principles extending compositional axioms tend to be either conservative over PAPA or exactly equivalent to the principle of global reflection over AA. It says that sentences provable in PAPA are true in the sense of the predicate TT. This in turn is equivalent to Δ0Δ0 induction for the compositional truth predicate which turns out to be a surprisingly robust theory.
The equivalences between nonconservative truth theories are typically proved by relatively direct ad hoc arguments. However, certain patterns seem common to these proofs. The first one is construction of various arithmetical partial truth predicates which provably in a given theory have better properties than the original truth predicate. The second one is deriving induction for these truth predicates from internal induction, a principle which says that for any arithmetical formula, the set of those elements for which that formula is satisfied under the truth predicate satisfies the usual induction axioms.
As an example of this phenomenon, we will present two proofs. First, we will show that global reflection principle is equivalent to local induction. Global reflection expresses that any sentence provable in PAPA is true. Local induction says that any predicate obtained by restricting truth predicate to sentences of a fixed syntactic complexity cc satisfies full induction. This is an observation due to Mateusz Łełyk and the author of this presentation.
The second example is a result by Ali Enayat who showed that CT0CT0, a theory compositional truth with Δ0Δ0 induction, is arithmetically equivalent to the theory of compositional truth together with internal induction and disjunctive correctness.
This talk is intended as a continuation of 'Tarski boundary II' presentation at the same seminar. However, we will try to avoid excessive assumptions on familiarity with the previous part.
- - - - Thursday, Jun 25, 2020 - - - -
- - - - Friday, Jun 26, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, June 26, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman for meeting id. Joel David Hamkins, Oxford University Categorical cardinals Zermelo famously characterized the models of second-order Zermelo-Fraenkel set theory ZFC2ZFC2 in his 1930 quasi-categoricity result asserting that the models of ZFC2ZFC2 are precisely those isomorphic to a rank-initial segment VκVκ of the cumulative set-theoretic universe VV cut off at an inaccessible cardinal κ.κ. I shall discuss the extent to which Zermelo's quasi-categoricity analysis can rise fully to the level of categoricity, in light of the observation that many of the VκVκ universes are categorically characterized by their sentences or theories. For example, if κκ is the smallest inaccessible cardinal, then up to isomorphism VκVκ is the unique model of ZFC2ZFC2 plus the sentence 'there are no inaccessible cardinals.' This cardinal κκ is therefore an instance of what we call a first-order sententially categorical cardinal. Similarly, many of the other inaccessible universes satisfy categorical extensions of ZFC2ZFC2 by a sentence or theory, either in first or second order. I shall thus introduce and investigate the categorical cardinals, a new kind of large cardinal. This is joint work with Robin Solberg (Oxford).
Next Week in Logic at CUNY:
- - - - Monday, Jun 29, 2020 - - - -
- - - - Tuesday, Jun 30, 2020 - - - -
- - - - Wednesday, Jul 1, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, July 1, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Zachiri McKenzie, Initial self-embeddings of models of set theory: Part II
In the 1973 paper 'Countable models of set theory', H. Friedman's investigation of embeddings between countable models of subsystems of ZF yields the following two striking results:
1. Every countable nonstandard model of PA is isomorphic to a proper initial segment of itself. 2. Every countable nonstandard model of a sufficiently strong subsystem of ZF is isomorphic to a proper initial segment that is a union of ranks of the original model.
Note that, in contrast to PA, in the context of set theory there are three alternative notions of 'initial segment': transitive subclass, transitive subclass that is closed under subsets and rank-initial segment. Paul Gorbow, in his Ph.D. thesis, systematically studies versions of H. Friedman's self-embedding that yield isomorphisms between a countable nonstandard model of set theory and a rank-initial segment of itself. In these two talks I will discuss recent joint work with Ali Enayat that investigates models of set theory that are isomorphic to a transitive subclass of itself. We call the maps witnessing these isomorphisms 'initial self-embeddings'. I will outline a proof of a refinement of H. Friedman's Theorem that guarantees the existence of initial self-embeddings for certain subsystems of ZF without the powerset axiom. I will then discuss several examples including a nonstandard model of ZFC minus the powerset axiom that admits no initial self-embedding, and models that separate the three different notions of self-embedding for models of set theory. Finally, I will discuss two interesting applications of our version of H. Freidman's Theorem. The first of these is a refinement of a result due to Quinsey that guarantees the existence of partially elementary proper transitive subclasses of non-standard models of ZF minus the powerset axiom. The second result shows that every countable model of ZF with a nonstandard natural number is isomorphic to a transitive subclass of the hereditarily countable sets of its own constructible universe.
- - - - Thursday, Jul 2, 2020 - - - -
- - - - Friday, Jul 3, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, July 3, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman for meeting id.
A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website, nylogic.github.io, take a look at the following for more seminar listings:
Online seminars and talks in Logic
A list of existing seminar series with talks available online, and links to recorded talks:
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Set theory seminar this week: Will Brian
Toronto Set Theory Seminar
6/21/2020 11:28:00
Hi everyone,
This week, Will Brian (UNC Charlotte) will speak in the seminar. His title and abstract can be found below.
Title: Limited-information strategies in Banach-Mazur games.
Abstract: The Banach-Mazur game is an infinite-length game played on a topological space X, in which two players take turns choosing members of an infinite decreasing sequence of open sets, the first player trying to ensure that the intersection of this sequence is empty, and the second that it is not. A limited-information strategy for one of the players is a game plan that, on any given move, depends on only a small part of the game's history. In this talk we will discuss Telgársky's conjecture, which asserts roughly that there must be topological spaces where winning strategies for the Banach-Mazur game cannot be too limited, but must rely on large parts of the game's history in a significant way. Recently, it was shown that this conjecture fails in models of set theory satisfying GCH + . In such models it is always possible for one player to code all information concerning a game's history into a small piece of it. We will discuss these so-called coding strategies, why assuming GCH + makes them work so well, and what can go wrong in other models of set theory.
The talk will take place on Friday, June 26 from 1:30-3:00 pm EDT on Zoom, follow the link below:
Dear all,
The seminar meets on Wednesday June 24th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Again, the program is not fixed yet, the backup is either me or Egbert
talking about some set theory. (Last time we were looking at the
triangle free Henson graph and some new proofs of Ramsey-like properties.)
Best,
David
Set theory seminar this week: David Schrittesser
Toronto Set Theory Seminar
6/15/2020 13:45:22
Hi everyone,
This week, David Schrittesser (KGRC, University of Vienna) will speak in the seminar.
Title: Higher degrees of madness
Abstract: The notion of mad family can be generalized by replacing the finite ideal by an iterated Fubini product of the finite ideal. While these ideals are more complicated both combinatorially and in terms of Borel complexity, it turns out that the same assumptions of Ramsey theoretic regularity can rule out their existence. We sketch a proof of this and some related results. This talk is a sequel to my last talk at the Fields Institute Seminar.
The talk will take place on Friday, June 19 from 1:30-3:00 pm EDT on Zoom, follow the link below:
Wednesday, June 17, 2:00pm
NOTE: 2:00pm START TIME
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Mateusz Łełyk, University of Warsaw Partial Reflection over Uniform Disquotational Truth
In the context of arithmetic, a reflection principle for a theory Th is a formal way of expressing that all theorems of Th are true. In the presence of a truth predicate for the language of Th this principle can be expressed as a single sentence (called the Global Reflection principle over Th) but most often is met in the form of a scheme consisting of all sentences of the form
∀x(ProvTh(ϕ(˙x))→ϕ(x)).∀x(ProvTh(ϕ(x˙))→ϕ(x)).
Obviously such a scheme is not provable in a consistent theory Th. Nevertheless, such soundness assertions are said to provide a natural and justified way of extending ones initial theory.
This perspective is nowadays very fruitfully exploited in the context of formal theories of truth. One of the most basic observations is that strong axioms for the notions of truth follow from formally weak types of axiomatizations modulo reflection principles. In such a way compositional axioms are consequences of the uniform disquotational scheme for for the truth predicate, which is
∀xT(ϕ(˙x))≡ϕ(x).∀xT(ϕ(x˙))≡ϕ(x).
The above observation is also used in the recent approach to ordinal analysis of theories of predicative strength by Lev Beklemishev and Fedor Pakhomov. The assignment of ordinal notations to theories proceeds via partial reflection principles (for formulae of a fixed ΣnΣn complexity) over (iterated) disquotational scheme. It becomes important to relate theories of this form to fragments of standard theories of truth, in particular the ones based on induction for restricted classes of formulae such as CT0CT0 (the theory of compositional truth with Δ0Δ0-induction for the extended language. The theory was discussed at length in Bartek Wcisło's talk). Beklemishev and Pakhomov leave the following open question:
Is Σ1Σ1-reflection principle over the uniform disquotational scheme provable in CT0CT0?
The main goal of our talk is to present the proof of the affirmative answer to this question. The result significantly improves the known fact on the provability of Global Reflection over PA in CT0CT0. During the talk, we explain the theoretical context described above including the information on how the result fits into Beklemishev-Pakhomov project. In the meantime we give a different proof of their characterisation of Δ0Δ0-reflection over the disquotational scheme.
Despite the proof-theoretical flavour of these results, our proofs rests on essentially model-theoretical techniques. The important ingredient is the Arithmetized Completeness Theorem.
- - - - Thursday, Jun 18, 2020 - - - -
- - - - Friday, Jun 19, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, June 19, 2pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Boban Velickovic, University of Paris 7
Strong guessing models
The notion of a guessing model introduced by Viale and Weiss. The principle GM(ω2,ω1)GM(ω2,ω1) asserts that there are stationary many guessing models of size ℵ1ℵ1 in HθHθ, for all large enough regular θθ. It follows from PFAPFA and implies many of its structural consequences, however it does not settle the value of the continuum. In search of higher of forcing axioms it is therefore natural to look for extensions and higher versions of this principle. We formulate and prove the consistency of one such statement that we call SGM+(ω3,ω1)SGM+(ω3,ω1). It has a number of important structural consequences:
- the tree property at ℵ2ℵ2 and ℵ3ℵ3 - the failure of various weak square principles - the Singular Cardinal Hypothesis - Mitchell’s Principle: the approachability ideal agrees with the non stationary ideal on the set of cof(ω1)cof(ω1) ordinals in ω2ω2 - Souslin’s Hypothesis - The negation of the weak Kurepa Hypothesis - Abraham’s Principles: every forcing which adds a subset of ω2ω2 either adds a real or collapses some cardinals, etc.
The results are joint with my PhD students Rahman Mohammadpour.
Next Week in Logic at CUNY:
- - - - Monday, Jun 22, 2020 - - - -
- - - - Tuesday, Jun 23, 2020 - - - -
- - - - Wednesday, Jun 24, 2020 - - - -
- - - - Thursday, Jun 25, 2020 - - - -
- - - - Friday, Jun 26, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, June 26, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman for meeting id. Joel David Hamkins, Oxford University TBA
- - - - Other Logic News - - - -
A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website, nylogic.github.io, take a look at the following for more seminar listings:
Online seminars and talks in Logic
A list of existing seminar series with talks available online, and links to recorded talks:
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Wednesday seminar
Prague Set Theory Seminar
6/12/2020 7:56:09
Dear all,
The seminar will meet again next week, on Wednesday June 17th at 11:00
in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor,
front building.
The program is not yet fixed, the default backup is either me or Egbert
Thuemmel talking about definable ideals on omega.
Best,
David
Set theory seminar this week: Jamal Kawach
Toronto Set Theory Seminar
6/8/2020 12:33:06
Hi everyone,
This week, Jamal Kawach (U of T) will speak in the seminar.
Title: Dual Ramsey theory for countable ordinals
Abstract: Using techniques from the theory of topological Ramsey spaces, we prove a dual Ramsey theorem for countable ordinals. Specifically, for each countable ordinal we define a topological Ramsey space of equivalence relations on which code equivalence relations on , up to a necessary restriction on the set of minimal representatives of the equivalence classes. This extends the classical dual Ramsey theorem of Carlson and Simpson. This is joint work with Stevo Todorcevic.
The talk will take place on June 12 from 1:30-3:00 pm EDT on Zoom, follow the link below:
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Zachiri McKenzie, Initial self-embeddings of models of set theory: Part II In the 1973 paper 'Countable models of set theory', H. Friedman's investigation of embeddings between countable models of subsystems of ZF yields the following two striking results:
1. Every countable nonstandard model of PA is isomorphic to a proper initial segment of itself. 2. Every countable nonstandard model of a sufficiently strong subsystem of ZF is isomorphic to a proper initial segment that is a union of ranks of the original model.
Note that, in contrast to PA, in the context of set theory there are three alternative notions of 'initial segment': transitive subclass, transitive subclass that is closed under subsets and rank-initial segment. Paul Gorbow, in his Ph.D. thesis, systematically studies versions of H. Friedman's self-embedding that yield isomorphisms between a countable nonstandard model of set theory and a rank-initial segment of itself. In these two talks I will discuss recent joint work with Ali Enayat that investigates models of set theory that are isomorphic to a transitive subclass of itself. We call the maps witnessing these isomorphisms 'initial self-embeddings'. I will outline a proof of a refinement of H. Friedman's Theorem that guarantees the existence of initial self-embeddings for certain subsystems of ZF without the powerset axiom. I will then discuss several examples including a nonstandard model of ZFC minus the powerset axiom that admits no initial self-embedding, and models that separate the three different notions of self-embedding for models of set theory. Finally, I will discuss two interesting applications of our version of H. Freidman's Theorem. The first of these is a refinement of a result due to Quinsey that guarantees the existence of partially elementary proper transitive subclasses of non-standard models of ZF minus the powerset axiom. The second result shows that every countable model of ZF with a nonstandard natural number is isomorphic to a transitive subclass of the hereditarily countable sets of its own constructible universe.
- - - - Thursday, Jun 11, 2020 - - - -
- - - - Friday, Jun 12, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, June 12, 2pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Michał Godziszewski, Munich Center for Mathematical Philosophy Michał Godziszewski, Munich Center for Mathematical Philosophy The Multiverse, Recursive Saturation and Well-Foundedness Mirage: Part II Recursive saturation, introduced by J. Barwise and J. Schlipf is a robust notion which has proved to be important for the study of nonstandard models (in particular, it is ubiquitous in the model theory of axiomatic theories of truth, e.g. in the topic of satisfaction classes, where one can show that if M⊨ZFCM⊨ZFC is a countable ωω-nonstandard model, then MM admits a satisfaction class iff MM is recursively saturated). V. Gitman and J. Hamkins showed in A Natural Model of the Multiverse Axioms that the collection of countable, recursively saturated models of set theory satisfy the so-called Hamkins's Multiverse Axioms. The property that forces all the models in the Multiverse to be recursively saturated is the so-called Well-Foundedness Mirage axiom which asserts that every universe is ωω-nonstandard from the perspective of some larger universe, or to be more precise, that: if a model MM is in the multiverse then there is a model NN in the multiverse such that MM is a set in NN and N⊨′M is ω−nonstandard.'N⊨′M is ω−nonstandard.'. Inspection of the proof led to a question if the recursive saturation could be avoided in the Multiverse by weakening the Well-Foundedness Mirage axiom. Our main results answer this in the positive. We give two different versions of the Well-Foundedness Mirage axiom - what we call Weak Well-Foundedness Mirage (saying that if MM is a model in the Multiverse then there is a model NN in the Multiverse such that M∈NM∈N and N⊨′M is nonstandard.'N⊨′M is nonstandard.'.) and Covering Well-Foundedness Mirage (saying that if MM is a model in the Multiverse then there is a model NN in the Multiverse with K∈NK∈N such that KK is an end-extension of MM and N⊨′K is ω−nonstandard.'N⊨′K is ω−nonstandard.'). I will present constructions of two different Multiverses satisfying these two weakened axioms. This is joint work with V. Gitman. T. Meadows and K. Williams.
Next Week in Logic at CUNY:
- - - - Monday, Jun 15, 2020 - - - -
- - - - Tuesday, Jun 16, 2020 - - - -
- - - - Wednesday, Jun 17, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, June 17, 2:00pm
NOTE: 2:00pm START TIME
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Mateusz Łełyk, University of Warsaw Partial Reflection over Uniform Disquotational Truth
In the context of arithmetic, a reflection principle for a theory Th is a formal way of expressing that all theorems of Th are true. In the presence of a truth predicate for the language of Th this principle can be expressed as a single sentence (called the Global Reflection principle over Th) but most often is met in the form of a scheme consisting of all sentences of the form
∀x(ProvTh(ϕ(˙x))→ϕ(x)).∀x(ProvTh(ϕ(x˙))→ϕ(x)).
Obviously such a scheme is not provable in a consistent theory Th. Nevertheless, such soundness assertions are said to provide a natural and justified way of extending ones initial theory.
This perspective is nowadays very fruitfully exploited in the context of formal theories of truth. One of the most basic observations is that strong axioms for the notions of truth follow from formally weak types of axiomatizations modulo reflection principles. In such a way compositional axioms are consequences of the uniform disquotational scheme for for the truth predicate, which is
∀xT(ϕ(˙x))≡ϕ(x).∀xT(ϕ(x˙))≡ϕ(x).
The above observation is also used in the recent approach to ordinal analysis of theories of predicative strength by Lev Beklemishev and Fedor Pakhomov. The assignment of ordinal notations to theories proceeds via partial reflection principles (for formulae of a fixed ΣnΣn complexity) over (iterated) disquotational scheme. It becomes important to relate theories of this form to fragments of standard theories of truth, in particular the ones based on induction for restricted classes of formulae such as CT0CT0 (the theory of compositional truth with Δ0Δ0-induction for the extended language. The theory was discussed at length in Bartek Wcisło's talk). Beklemishev and Pakhomov leave the following open question:
Is Σ1Σ1-reflection principle over the uniform disquotational scheme provable in CT0CT0?
The main goal of our talk is to present the proof of the affirmative answer to this question. The result significantly improves the known fact on the provability of Global Reflection over PA in CT0CT0. During the talk, we explain the theoretical context described above including the information on how the result fits into Beklemishev-Pakhomov project. In the meantime we give a different proof of their characterisation of Δ0Δ0-reflection over the disquotational scheme.
Despite the proof-theoretical flavour of these results, our proofs rests on essentially model-theoretical techniques. The important ingredient is the Arithmetized Completeness Theorem.
- - - - Thursday, Jun 18, 2020 - - - -
- - - - Friday, Jun 19, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, June 19, 2pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Boban Velickovic University of Paris 7
TBA
- - - - Other Logic News - - - -
A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website, nylogic.github.io, take a look at the following for more seminar listings:
Online seminars and talks in Logic
A list of existing seminar series with talks available online, and links to recorded talks:
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
This Week in Logic at CUNY
6/1/2020 20:41:19
This Week in Logic at CUNY:
- - - - Monday, Jun 1, 2020 - - - -
- - - - Tuesday, Jun 2, 2020 - - - -
- - - - Wednesday, Jun 3, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, June 3, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Zachiri McKenzie, Initial self-embeddings of models of set theory: Part I
In the 1973 paper 'Countable models of set theory', H. Friedman's investigation of embeddings between countable models of subsystems of ZF yields the following two striking results:
1. Every countable nonstandard model of PA is isomorphic to a proper initial segment of itself. 2. Every countable nonstandard model of a sufficiently strong subsystem of ZF is isomorphic to a proper initial segment that is a union of ranks of the original model.
Note that, in contrast to PA, in the context of set theory there are three alternative notions of 'initial segment': transitive subclass, transitive subclass that is closed under subsets and rank-initial segment. Paul Gorbow, in his Ph.D. thesis, systematically studies versions of H. Friedman's self-embedding that yield isomorphisms between a countable nonstandard model of set theory and a rank-initial segment of itself. In these two talks I will discuss recent joint work with Ali Enayat that investigates models of set theory that are isomorphic to a transitive subclass of itself. We call the maps witnessing these isomorphisms 'initial self-embeddings'. I will outline a proof of a refinement of H. Friedman's Theorem that guarantees the existence of initial self-embeddings for certain subsystems of ZF without the powerset axiom. I will then discuss several examples including a nonstandard model of ZFC minus the powerset axiom that admits no initial self-embedding, and models that separate the three different notions of self-embedding for models of set theory. Finally, I will discuss two interesting applications of our version of H. Freidman's Theorem. The first of these is a refinement of a result due to Quinsey that guarantees the existence of partially elementary proper transitive subclasses of non-standard models of ZF minus the powerset axiom. The second result shows that every countable model of ZF with a nonstandard natural number is isomorphic to a transitive subclass of the hereditarily countable sets of its own constructible universe.
- - - - Thursday, Jun 4, 2020 - - - -
- - - - Friday, Jun 5, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, June 5, 2pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Michał Godziszewski, Munich Center for Mathematical Philosophy TBA
Next Week in Logic at CUNY:
- - - - Monday, Jun 8, 2020 - - - -
- - - - Tuesday, Jun 9, 2020 - - - -
- - - - Wednesday, Jun 10, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, June 10, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Zachiri McKenzie, Initial self-embeddings of models of set theory: Part II In the 1973 paper 'Countable models of set theory', H. Friedman's investigation of embeddings between countable models of subsystems of ZF yields the following two striking results:
1. Every countable nonstandard model of PA is isomorphic to a proper initial segment of itself. 2. Every countable nonstandard model of a sufficiently strong subsystem of ZF is isomorphic to a proper initial segment that is a union of ranks of the original model.
Note that, in contrast to PA, in the context of set theory there are three alternative notions of 'initial segment': transitive subclass, transitive subclass that is closed under subsets and rank-initial segment. Paul Gorbow, in his Ph.D. thesis, systematically studies versions of H. Friedman's self-embedding that yield isomorphisms between a countable nonstandard model of set theory and a rank-initial segment of itself. In these two talks I will discuss recent joint work with Ali Enayat that investigates models of set theory that are isomorphic to a transitive subclass of itself. We call the maps witnessing these isomorphisms 'initial self-embeddings'. I will outline a proof of a refinement of H. Friedman's Theorem that guarantees the existence of initial self-embeddings for certain subsystems of ZF without the powerset axiom. I will then discuss several examples including a nonstandard model of ZFC minus the powerset axiom that admits no initial self-embedding, and models that separate the three different notions of self-embedding for models of set theory. Finally, I will discuss two interesting applications of our version of H. Freidman's Theorem. The first of these is a refinement of a result due to Quinsey that guarantees the existence of partially elementary proper transitive subclasses of non-standard models of ZF minus the powerset axiom. The second result shows that every countable model of ZF with a nonstandard natural number is isomorphic to a transitive subclass of the hereditarily countable sets of its own constructible universe.
- - - - Thursday, Jun 11, 2020 - - - -
- - - - Friday, Jun 12, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, June 12, 2pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Michał Godziszewski, Munich Center for Mathematical Philosophy TBA
- - - - Other Logic News - - - -
A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website, nylogic.github.io, take a look at the following for more seminar listings:
Online seminars and talks in Logic
A list of existing seminar series with talks available online, and links to recorded talks:
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
UPDATE - This Week in Logic at CUNY
This Week in Logic at CUNY
5/25/2020 23:23:22
A correction - this Wednesday's talk in the MOPA seminar will take place at 2pm, rather than the usual 7pm.
Best,
Jonas
This Week in Logic at CUNY:
- - - - Monday, May 25, 2020 - - - -
- - - - Tuesday, May 26, 2020 - - - -
- - - - Wednesday, May 27, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, May 27, 2:00pm
NOTE: New time this week only
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Bartosz Wcisło, University of Warsaw Tarski boundary II
Truth theories investigate the notion of truth with axiomatic methods. To a fixed base theory (typically Peano Arithmetic PAPA) we add a unary predicate T(x)T(x) with the intended interpretation 'xx is a (code of a) true sentence.' Then we analyse how adding various possible sets of axioms for that predicate affects its behaviour.
One of the aspects we are trying to understand is which truth-theoretic principles make the added truth predicate 'strong' in that the resulting theory is not conservative over the base theory. Ali Enayat proposed to call this 'demarcating line' between conservative and non-conservative truth theories 'the Tarski boundary.'
Research on Tarski boundary revealed that natural truth theoretic principles extending compositional axioms tend to be either conservative over PAPA or exactly equivalent to the principle of global reflection over PAPA. It says that sentences provable in PAPA are true in the sense of the predicate TT. This in turn is equivalent to Δ0Δ0 induction for the compositional truth predicate which turns out to be a surprisingly robust theory.
In our talk, we will try to sketch proofs representative of research on Tarski boundary. We will present the proof by Enayat and Visser showing that the compositional truth predicate is conservative over PAPA. We will also try to discuss how this proof forms a robust basis for further conservativeness results.
On the non-conservative side of Tarski boundary, the picture seems less organised, since more arguments are based on ad hoc constructions. However, we will try to show some themes which occur rather repeatedly in these proofs: iterated truth predicates and the interplay between properties of good truth-theoretic behaviour and induction. To this end, we will present the argument that disjunctive correctness together with the internal induction principle for a compositional truth predicate yields the same consequences as Δ0Δ0-induction for the compositional truth predicate (as proved by Ali Enayat) and that it shares arithmetical consequences with global reflection. The presented results are currently known to be suboptimal.
This talk is intended as a continuation of 'Tarski boundary' presentation. However, we will try to avoid excessive assumptions on familiarity with the previous part.
- - - - Thursday, May 28, 2020 - - - -
- - - - Friday, May 29, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 29, 2pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Kameryn Williams, University of Hawai‘i at Mānoa The geology of inner mantles
An inner model is a ground if V is a set forcing extension of it. The intersection of the grounds is the mantle, an inner model of ZFC which enjoys many nice properties. Fuchs, Hamkins, and Reitz showed that the mantle is highly malleable. Namely, they showed that every model of set theory is the mantle of a bigger, better universe of sets. This then raises the possibility of iterating the definition of the mantle—the mantle, the mantle of the mantle, and so on, taking intersections at limit stages—to obtain even deeper inner models. Let's call the inner models in this sequence the inner mantles.
In this talk I will present some results about the sequence of inner mantles, answering some questions of Fuchs, Hamkins, and Reitz. Specifically, I will present the following results, analogues of classic results about the sequence of iterated HODs.
1. (Joint with Reitz) Consider a model of set theory and consider an ordinal eta in that model. Then this model has a class forcing extension whose eta-th inner mantle is the model we started out with, where the sequence of inner mantles does not stabilize before eta.
2. It is consistent that the omega-th inner mantle is an inner model of ZF + ¬AC.
3. It is consistent that the omega-th inner mantle is not a definable class, and indeed fails to satisfy Collection.
Next Week in Logic at CUNY:
- - - - Monday, Jun 1, 2020 - - - -
- - - - Tuesday, Jun 2, 2020 - - - -
- - - - Wednesday, Jun 3, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, June 3, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Zachiri McKenzie, Initial self-embeddings of models of set theory: Part I
In the 1973 paper 'Countable models of set theory', H. Friedman's investigation of embeddings between countable models of subsystems of ZF yields the following two striking results:
1. Every countable nonstandard model of PA is isomorphic to a proper initial segment of itself. 2. Every countable nonstandard model of a sufficiently strong subsystem of ZF is isomorphic to a proper initial segment that is a union of ranks of the original model.
Note that, in contrast to PA, in the context of set theory there are three alternative notions of 'initial segment': transitive subclass, transitive subclass that is closed under subsets and rank-initial segment. Paul Gorbow, in his Ph.D. thesis, systematically studies versions of H. Friedman's self-embedding that yield isomorphisms between a countable nonstandard model of set theory and a rank-initial segment of itself. In these two talks I will discuss recent joint work with Ali Enayat that investigates models of set theory that are isomorphic to a transitive subclass of itself. We call the maps witnessing these isomorphisms 'initial self-embeddings'. I will outline a proof of a refinement of H. Friedman's Theorem that guarantees the existence of initial self-embeddings for certain subsystems of ZF without the powerset axiom. I will then discuss several examples including a nonstandard model of ZFC minus the powerset axiom that admits no initial self-embedding, and models that separate the three different notions of self-embedding for models of set theory. Finally, I will discuss two interesting applications of our version of H. Freidman's Theorem. The first of these is a refinement of a result due to Quinsey that guarantees the existence of partially elementary proper transitive subclasses of non-standard models of ZF minus the powerset axiom. The second result shows that every countable model of ZF with a nonstandard natural number is isomorphic to a transitive subclass of the hereditarily countable sets of its own constructible universe.
- - - - Thursday, Jun 4, 2020 - - - -
- - - - Friday, Jun 5, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, June 5, 2pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Michał Godziszewski, Munich Center for Mathematical Philosophy TBA
- - - - Other Logic News - - - -
A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website, nylogic.github.io, take a look at the following for more seminar listings:
Online seminars and talks in Logic
A list of existing seminar series with talks available online, and links to recorded talks:
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
This Week in Logic at CUNY
This Week in Logic at CUNY
5/25/2020 21:55:51
Hi everyone,
The CUNY semester is coming to an end. However, a number of seminars have plans to continue into the summer months. Regular weekly mailings of "This Week in Logic at CUNY" will continue as long as we have events to report!
Best regards,
Jonas
This Week in Logic at CUNY:
- - - - Monday, May 25, 2020 - - - -
- - - - Tuesday, May 26, 2020 - - - -
- - - - Wednesday, May 27, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, May 27, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Bartosz Wcisło, University of Warsaw Tarski boundary II
Truth theories investigate the notion of truth with axiomatic methods. To a fixed base theory (typically Peano Arithmetic PAPA) we add a unary predicate T(x)T(x) with the intended interpretation 'xx is a (code of a) true sentence.' Then we analyse how adding various possible sets of axioms for that predicate affects its behaviour.
One of the aspects we are trying to understand is which truth-theoretic principles make the added truth predicate 'strong' in that the resulting theory is not conservative over the base theory. Ali Enayat proposed to call this 'demarcating line' between conservative and non-conservative truth theories 'the Tarski boundary.'
Research on Tarski boundary revealed that natural truth theoretic principles extending compositional axioms tend to be either conservative over PAPA or exactly equivalent to the principle of global reflection over PAPA. It says that sentences provable in PAPA are true in the sense of the predicate TT. This in turn is equivalent to Δ0Δ0 induction for the compositional truth predicate which turns out to be a surprisingly robust theory.
In our talk, we will try to sketch proofs representative of research on Tarski boundary. We will present the proof by Enayat and Visser showing that the compositional truth predicate is conservative over PAPA. We will also try to discuss how this proof forms a robust basis for further conservativeness results.
On the non-conservative side of Tarski boundary, the picture seems less organised, since more arguments are based on ad hoc constructions. However, we will try to show some themes which occur rather repeatedly in these proofs: iterated truth predicates and the interplay between properties of good truth-theoretic behaviour and induction. To this end, we will present the argument that disjunctive correctness together with the internal induction principle for a compositional truth predicate yields the same consequences as Δ0Δ0-induction for the compositional truth predicate (as proved by Ali Enayat) and that it shares arithmetical consequences with global reflection. The presented results are currently known to be suboptimal.
This talk is intended as a continuation of 'Tarski boundary' presentation. However, we will try to avoid excessive assumptions on familiarity with the previous part.
- - - - Thursday, May 28, 2020 - - - -
- - - - Friday, May 29, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 29, 2pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Kameryn Williams, University of Hawai‘i at Mānoa The geology of inner mantles
An inner model is a ground if V is a set forcing extension of it. The intersection of the grounds is the mantle, an inner model of ZFC which enjoys many nice properties. Fuchs, Hamkins, and Reitz showed that the mantle is highly malleable. Namely, they showed that every model of set theory is the mantle of a bigger, better universe of sets. This then raises the possibility of iterating the definition of the mantle—the mantle, the mantle of the mantle, and so on, taking intersections at limit stages—to obtain even deeper inner models. Let's call the inner models in this sequence the inner mantles.
In this talk I will present some results about the sequence of inner mantles, answering some questions of Fuchs, Hamkins, and Reitz. Specifically, I will present the following results, analogues of classic results about the sequence of iterated HODs.
1. (Joint with Reitz) Consider a model of set theory and consider an ordinal eta in that model. Then this model has a class forcing extension whose eta-th inner mantle is the model we started out with, where the sequence of inner mantles does not stabilize before eta.
2. It is consistent that the omega-th inner mantle is an inner model of ZF + ¬AC.
3. It is consistent that the omega-th inner mantle is not a definable class, and indeed fails to satisfy Collection.
Next Week in Logic at CUNY:
- - - - Monday, Jun 1, 2020 - - - -
- - - - Tuesday, Jun 2, 2020 - - - -
- - - - Wednesday, Jun 3, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, June 3, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Zachiri McKenzie, Initial self-embeddings of models of set theory: Part I
In the 1973 paper 'Countable models of set theory', H. Friedman's investigation of embeddings between countable models of subsystems of ZF yields the following two striking results:
1. Every countable nonstandard model of PA is isomorphic to a proper initial segment of itself. 2. Every countable nonstandard model of a sufficiently strong subsystem of ZF is isomorphic to a proper initial segment that is a union of ranks of the original model.
Note that, in contrast to PA, in the context of set theory there are three alternative notions of 'initial segment': transitive subclass, transitive subclass that is closed under subsets and rank-initial segment. Paul Gorbow, in his Ph.D. thesis, systematically studies versions of H. Friedman's self-embedding that yield isomorphisms between a countable nonstandard model of set theory and a rank-initial segment of itself. In these two talks I will discuss recent joint work with Ali Enayat that investigates models of set theory that are isomorphic to a transitive subclass of itself. We call the maps witnessing these isomorphisms 'initial self-embeddings'. I will outline a proof of a refinement of H. Friedman's Theorem that guarantees the existence of initial self-embeddings for certain subsystems of ZF without the powerset axiom. I will then discuss several examples including a nonstandard model of ZFC minus the powerset axiom that admits no initial self-embedding, and models that separate the three different notions of self-embedding for models of set theory. Finally, I will discuss two interesting applications of our version of H. Freidman's Theorem. The first of these is a refinement of a result due to Quinsey that guarantees the existence of partially elementary proper transitive subclasses of non-standard models of ZF minus the powerset axiom. The second result shows that every countable model of ZF with a nonstandard natural number is isomorphic to a transitive subclass of the hereditarily countable sets of its own constructible universe.
- - - - Thursday, Jun 4, 2020 - - - -
- - - - Friday, Jun 5, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, June 5, 2pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Michał Godziszewski, Munich Center for Mathematical Philosophy TBA
- - - - Other Logic News - - - -
A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website, nylogic.github.io, take a look at the following for more seminar listings:
Online seminars and talks in Logic
A list of existing seminar series with talks available online, and links to recorded talks:
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Set theory seminar this week: Michael Hrusak
Toronto Set Theory Seminar
5/25/2020 10:59:31
Hi everyone,
This Friday, Michael Hrusak (UNAM) will speak in our seminar on the Invariant Ideal Axiom.
Abstract: We introduce the Invariant Ideal Axiom and discuss its impact on the structure of countable topological groups. (joint work with Alexander Shibakov)
The talk will take place on May 29 from 1:30-3:00 pm EDT on Zoom, follow the link below:
Set theory seminar this week: Vinicius de Oliveira Rodrigues
Toronto Set Theory Seminar
5/18/2020 9:32:37
Hi everyone,
This week, the seminar will host Vinicius de Oliveira Rodrigues (University of São Paulo) who will speak about "Pseudocompact hyperspaces of Isbell-Mrówka spaces." The talk will feature some new results obtained after his talk from November.
Abstract: J. Ginsburg has asked what is the relation between the pseudocompactness of the -th power of a topological space and the pseudocompactness of its Vietoris Hyperspace, . M. Hrusak, I. Martínez-Ruiz and F. Hernandez-Hernandez studied this question restricted to Isbell-Mrówka spaces, that is, spaces of the form where A is an almost disjoint family. Regarding these spaces, if is pseudocompact, then is also pseudocompact, and is pseudocompact iff is a MAD family. They showed that if the cardinal characteristic is , then for every MAD family , is pseudocompact, and if the cardinal characteristic is less than , there exists a MAD family such that is not pseudocompact. They asked if there exists a MAD family (in ZFC) such that is pseudocompact.
In this talk, we present some new results on the (consistent) existence of MAD families whose hyperspaces of their Isbell-Mrówka spaces are (or are not) pseudocompact by constructing new examples. Moreover, we give some combinatorial equivalences for every Isbell-Mrówka space from a MAD family having pseudocompact hyperspace. This is a joint work with, O. Guzman, M. Hrusak, S. Todorcevic and A. Tomita.
The talk will take place this Friday, May 22, from 1:30-3:00 pm EDT on Zoom, follow the link below:
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Ali Enayat, University of Gothenburg Recursively saturated models of set theory and their close relatives: Part II
A model MM of set theory is said to be 'condensable' if there is an 'ordinal' αα of MM such that the rank initial segment of MM determined by αα is both isomorphic to MM, and an elementary submodel of MM for infinitary formulae appearing in the well-founded part of MM. Clearly if MM is condensable, then MM is ill-founded. The work of Barwise and Schlipf in the mid 1970s showed that countable recursively saturated models of ZF are condensable.
In this two-part talk, we present a number of new results related to condensable models, including the following two theorems.
Theorem 1. Assuming that there is a well-founded model of ZFC plus 'there is an inaccessible cardinal', there is a condensable model MM of ZFC which has the property that every definable element of MM is in the well-founded part of MM (in particular, MM is ωω-standard, and therefore not recursively saturated).
Theorem 2. The following are equivalent for an ill-founded model MM of ZF of any cardinality: (a) MM is expandable to Gödel-Bernays class theory plus Δ11Δ11-Comprehension. (b) There is a cofinal subset of 'ordinals' αα of MM such that the rank initial segment of MM determined by αα is an elementary submodel of MM for infinitary formulae appearing in the well-founded part of M.M. Moreover, if MM is a countable ill-founded model of ZFC, then conditions (a) and (b) above are equivalent to: (c) MM is expandable to Gödel-Bernays class theory plus Δ11Δ11-Comprehension + Σ12Σ21-Choice.
Next Week in Logic at CUNY:
- - - - Monday, May 25, 2020 - - - -
- - - - Tuesday, May 26, 2020 - - - -
- - - - Wednesday, May 27, 2020 - - - -
- - - - Thursday, May 28, 2020 - - - -
- - - - Friday, May 29, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 22, 2pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Kameryn Williams, University of Hawai‘i at Mānoa TBA
- - - - Other Logic News - - - -
A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website, nylogic.github.io, take a look at the following for more seminar listings:
Online seminars and talks in Logic
A list of existing seminar series with talks available online, and links to recorded talks:
There is a well-known close logical connection between PA and finite set theory. Is there a set theory that corresponds in an analogous way to bounded arithmetic IΔ0IΔ0? I propose a candidate for such a theory, called IΔ0SIΔ0S, and consider the questions: what set-theoretic axioms can it prove? And given a model M of IΔ0IΔ0 is there a model of IΔ0SIΔ0S whose ordinals are isomorphic to M? The answer is yes if M is a model of Exp; to obtain the answer we use a new way of coding sets by numbers.
- - - - Thursday, May 14, 2020 - - - -
- - - - Friday, May 15, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 15, 2pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Ali Enayat, University of Gothenburg Recursively saturated models of set theory and their close relatives: Part I
A model MM of set theory is said to be 'condensable' if there is an 'ordinal' αα of MM such that the rank initial segment of MM determined by αα is both isomorphic to MM, and an elementary submodel of MM for infinitary formulae appearing in the well-founded part of MM. Clearly if MM is condensable, then MM is ill-founded. The work of Barwise and Schlipf in the mid 1970s showed that countable recursively saturated models of ZF are condensable.
In this two-part talk, we present a number of new results related to condensable models, including the following two theorems.
Theorem 1. Assuming that there is a well-founded model of ZFC plus 'there is an inaccessible cardinal', there is a condensable model MM of ZFC which has the property that every definable element of MM is in the well-founded part of MM (in particular, MM is ωω-standard, and therefore not recursively saturated).
Theorem 2. The following are equivalent for an ill-founded model MM of ZF of any cardinality: (a) MM is expandable to Gödel-Bernays class theory plus Δ11Δ11-Comprehension. (b) There is a cofinal subset of 'ordinals' αα of MM such that the rank initial segment of MM determined by αα is an elementary submodel of MM for infinitary formulae appearing in the well-founded part of M.M. Moreover, if MM is a countable ill-founded model of ZFC, then conditions (a) and (b) above are equivalent to: (c) MM is expandable to Gödel-Bernays class theory plus Δ11Δ11-Comprehension + Σ12Σ21-Choice.
Next Week in Logic at CUNY:
- - - - Monday, May 18, 2020 - - - -
- - - - Tuesday, May 19, 2020 - - - -
- - - - Wednesday, May 20, 2020 - - - -
- - - - Thursday, May 21, 2020 - - - -
- - - - Friday, May 22, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 15, 2pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Ali Enayat, University of Gothenburg Recursively saturated models of set theory and their close relatives: Part II
A model MM of set theory is said to be 'condensable' if there is an 'ordinal' αα of MM such that the rank initial segment of MM determined by αα is both isomorphic to MM, and an elementary submodel of MM for infinitary formulae appearing in the well-founded part of MM. Clearly if MM is condensable, then MM is ill-founded. The work of Barwise and Schlipf in the mid 1970s showed that countable recursively saturated models of ZF are condensable.
In this two-part talk, we present a number of new results related to condensable models, including the following two theorems.
Theorem 1. Assuming that there is a well-founded model of ZFC plus 'there is an inaccessible cardinal', there is a condensable model MM of ZFC which has the property that every definable element of MM is in the well-founded part of MM (in particular, MM is ωω-standard, and therefore not recursively saturated).
Theorem 2. The following are equivalent for an ill-founded model MM of ZF of any cardinality: (a) MM is expandable to Gödel-Bernays class theory plus Δ11Δ11-Comprehension. (b) There is a cofinal subset of 'ordinals' αα of MM such that the rank initial segment of MM determined by αα is an elementary submodel of MM for infinitary formulae appearing in the well-founded part of M.M. Moreover, if MM is a countable ill-founded model of ZFC, then conditions (a) and (b) above are equivalent to: (c) MM is expandable to Gödel-Bernays class theory plus Δ11Δ11-Comprehension + Σ12Σ21-Choice.
- - - - Other Logic News - - - -
A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website, nylogic.github.io, take a look at the following for more seminar listings:
Online seminars and talks in Logic
A list of existing seminar series with talks available online, and links to recorded talks:
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Set theory seminar this Friday: Dima Sinapova
Toronto Set Theory Seminar
5/5/2020 8:00:00
Hi everyone,
This week, we will have Dima Sinapova speaking in the seminar. Her talk is entitled "Iteration, reflection, and Prikry forcing."
Abstract: There is an inherent tension between stationary reflection and the failure of SCH. The former is a compactness type principle that follows from large cardinals. The latter is an instance of incompactness, and usually obtained using Prikry forcing. We describe a Prikry style iteration, and use it to force stationary reflection in the presence of not SCH. Then we discuss the situation at smaller cardinals. This is joint work with Alejandro Poveda and Assaf Rinot.
The talk will take place this Friday, May 8, from 1:30-3:00 pm EDT on Zoom, follow the link below:
IMPORTANT NOTE: Due to an upgrade in Zoom security features, we have a new Zoom link and Meeting ID. Please change your bookmarks accordingly.
See you there,
Bill Chen
This Week in Logic at CUNY
This Week in Logic at CUNY
5/4/2020 0:29:42
Hi everyone,
I'm pleased to pass along the following announcement from Joel David Hamkins:
Oxford Set Theory Seminar I am starting the Oxford Set Theory Seminar, to be held online via Zoom for the foreseeable future. All set theorists are welcome to participate. You can find a schedule of this term's talks at http://jdh.hamkins.org/oxford-set-theory-seminar/ .
-Joel
Best, Jonas
This Week in Logic at CUNY:
- - - - Monday, May 4, 2020 - - - -
- - - - Tuesday, May 5, 2020 - - - -
- - - - Wednesday, May 6, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, May 6, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
May 6 Ali Enayat, University of Gothenburg The Barwise-Schlipf characterization of recursive saturation of models of PA: Part II
The subject of this two-part talk is a 1975 Barwise-Schlipf landmark paper, whose main theorem asserts that a nonstandard model M of PA is recursively saturated iff M has an expansion to a model of the subsystem Δ11−CA0Δ11−CA0 of second order arithmetic. The impression one gets from reading the Barwise-Schlipf paper is that the left-to-right direction of the theorem is deep since it relies on sophisticated techniques from admissible set theory, and that the other direction is fairly routine.
As it turns out, the exact opposite is the case: the left-to-right direction of the Barwise-Schlipf theorem lends itself to a proof from first principles (as observed independently by Jonathan Stavi and Sol Feferman not long after the appearance of the Barwise-Schmerl paper); and moreover, as recently shown in my joint work with Jim Schmerl, there is a crucial error in the Barwise-Schlipf proof of the right-to-left direction of the theorem, an error that can be circumvented by a rather nontrivial argument. As I will explain, certain results from the joint work of Matt Kaufmann and Jim Schmerl in the mid-1980s on 'lofty' models of arithmetic come in handy for the analysis of the error, and for circumventing it.
In part I, after going over some history, and preliminaries, I will discuss (1) the gap in the Barwise-Schlipf paper, and (2) the aforementioned Feferman-Stavi proof. In part II, I will focus on how the gap can be circumvented with a proof strategy very different from that Barwise and Schlipf.
- - - - Thursday, May 7, 2020 - - - -
- - - - Friday, May 8, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 8, 2pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Sandra Müller, University of Vienna TBA
Next Week in Logic at CUNY:
- - - - Monday, May 11, 2020 - - - -
- - - - Tuesday, May 12, 2020 - - - -
- - - - Wednesday, May 13, 2020 - - - -
- - - - Thursday, May 14, 2020 - - - -
- - - - Friday, May 15, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 15, 2pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Ali Enayat, University of Gothenburg Recursively saturated models of set theory and their close relatives: Part I
A model MM of set theory is said to be 'condensable' if there is an 'ordinal' αα of MM such that the rank initial segment of MM determined by αα is both isomorphic to MM, and an elementary submodel of MM for infinitary formulae appearing in the well-founded part of MM. Clearly if MM is condensable, then MM is ill-founded. The work of Barwise and Schlipf in the mid 1970s showed that countable recursively saturated models of ZF are condensable.
In this two-part talk, we present a number of new results related to condensable models, including the following two theorems.
Theorem 1. Assuming that there is a well-founded model of ZFC plus 'there is an inaccessible cardinal', there is a condensable model MM of ZFC which has the property that every definable element of MM is in the well-founded part of MM (in particular, MM is ωω-standard, and therefore not recursively saturated).
Theorem 2. The following are equivalent for an ill-founded model MM of ZF of any cardinality: (a) MM is expandable to Gödel-Bernays class theory plus Δ11Δ11-Comprehension. (b) There is a cofinal subset of 'ordinals' αα of MM such that the rank initial segment of MM determined by αα is an elementary submodel of MM for infinitary formulae appearing in the well-founded part of M.M. Moreover, if MM is a countable ill-founded model of ZFC, then conditions (a) and (b) above are equivalent to: (c) MM is expandable to Gödel-Bernays class theory plus Δ11Δ11-Comprehension + Σ12Σ21-Choice.
- - - - Other Logic News - - - -
A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website, nylogic.github.io, take a look at the following for more seminar listings:
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Wednesday seminar
Prague Set Theory Seminar
5/3/2020 14:58:37
Dear all,
There are still no seminar in Prague next week. However, the PhD defence
of Jan Grebik will take place on Tuesday, May 5th at 10:00 via Zoom,
https://cesnet.zoom.us/j/98441831119
The defence is public, guests are welcome and expected. More info here:
https://is.cuni.cz/studium/szz_st/index.php?do=detail_kom&kom=28035&term=587734
Let me also add info on the zoom seminars in Jerusalem and Wroclaw next
week, these may be relevant for our usual audience.
Ziemowit Kostana -- Cohen-like poset for adding Fraisse limits
Tuesday May 5, 17:00 CEST
https://us02web.zoom.us/j/85273088816?pwd=RnRJcXc1YnpWL3R2Y1JRWkVGRUJxUT09
Meeting ID: 852 7308 8816
Password: 978458
There exist a natural forcing notion which turns given countable set
into a Fraisse limit of a given Fraisse class. This long-known
phenomenon provided a rough intuition that Fraisse limits, as "generic
structures", have some connections with forcing. The goal of the talk is
to look at some particular instances and possible applications of this idea.
Tsoor Plotnikov -- Proper forcings and side conditions forcings (continued)
Monday May 4, 10:00am CEST
Meeting ID: 995 0029 0990
Password: 789132
Here are links to the files containing the write up of the two previous
talks:
https://drive.google.com/file/d/1GkkMmUA8usD-vVw0ybX1M5_eTZhgURcu/view?usp=sharing
https://drive.google.com/file/d/1izDqHGMFcGiQw75TvtyD4jzvi7YS-8EW/view?usp=sharing
Alejandro Poveda -- Sigma-Prikry forcings and their iterations
Wednesday May 6, at 10:00 CEST
Meeting ID: 243 676 331 (no password)
In a joint project with A. Rinot and D. Sinapova we introduce a class of
notions of forcing which we call $\Sigma$-Prikry, and show that many of
the known Prikry-type notions of forcing that centers around singular
cardinals of countable cofinality are $\Sigma$-Prikry. Among these
examples one may find Prikry forcing and its supercompact version,
Gitik-Sharon forcing or the Extender Based Prikry forcing due to Gitik
and Magidor.
Our first result shows that there is a functor $\mathbb{A}(\cdot,\cdot)$
which, given a $\Sigma$-Prikry poset $\mathbb P$ and a name for a
non-reflecting stationary set $\dot{T}$, yields a $\Sigma$-Prikry poset
$\mathbb{A}(\mathbb{P},\dot{T})$ that projects onto $\mathbb P$ and
kills the stationarity of $T$. Afterwards, we develop a viable iteration
scheme for $\Sigma$-Prikry posets.
In this talk I pretend to give an overview of this theory and, if time
permits, present the very first application of the method: namely, the
consistency of a failure of the SCH_\kappa with
$Refl(<\omega,\kappa^+)$, where $\kappa$ is a strong limit singular
cardinal of countable cofinality.
Best,
David
Set theory seminar this week: Paul Szeptycki
Toronto Set Theory Seminar
4/29/2020 19:34:05
Hi everyone,
This Friday, Paul Szeptycki will speak in the seminar. His talk is entitled "Strong convergence properties and an example from a sequence."
Abstract: We present an example of a space constructed from answering some questions of Arhangel'skii. Coauthors Bill Chen and Cesar Corral-Rojas.
The talk will take place this Friday, May 1, from 1:30-3:00 pm EDT on Zoom, follow the link below:
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
April 29 Ali Enayat, University of Gothenburg The Barwise-Schlipf characterization of recursive saturation of models of PA
The subject of this talk is a 1975 Barwise-Schlipf landmark paper, whose main theorem asserts that a nonstandard model M of PA is recursively saturated iff M has an expansion to a model of the subsystem Δ11−CA0Δ11−CA0 of second order arithmetic. The impression one gets from reading the Barwise-Schlipf paper is that the left-to-right direction of the theorem is deep since it relies on sophisticated techniques from admissible set theory, and that the other direction is fairly routine.
As it turns out, the exact opposite is the case: the left-to-right direction of the Barwise-Schlipf theorem lends itself to a proof from first principles (as observed independently by Jonathan Stavi and Sol Feferman not long after the appearance of the Barwise-Schmerl paper); and moreover, as recently shown in my joint work with Jim Schmerl, there is a crucial error in the Barwise-Schlipf proof of the right-to-left direction of the theorem, an error that can be circumvented by a rather nontrivial argument. As I will explain, certain results from the joint work of Matt Kaufmann and Jim Schmerl in the mid-1980s on 'lofty' models of arithmetic come in handy for the analysis of the error, and for circumventing it.
- - - - Thursday, Apr 30, 2020 - - - -
- - - - Friday, May 1, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 1, 2pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Joan Bagaria Universitat de Barcelona TBA
Next Week in Logic at CUNY:
- - - - Monday, May 4, 2020 - - - -
- - - - Tuesday, May 5, 2020 - - - -
- - - - Wednesday, May 6, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, May 6, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
May 6 Ali Enayat, University of Gothenburg The Barwise-Schlipf characterization of recursive saturation of models of PA, part 2
The subject of this talk is a 1975 Barwise-Schlipf landmark paper, whose main theorem asserts that a nonstandard model M of PA is recursively saturated iff M has an expansion to a model of the subsystem Δ11−CA0Δ11−CA0 of second order arithmetic. The impression one gets from reading the Barwise-Schlipf paper is that the left-to-right direction of the theorem is deep since it relies on sophisticated techniques from admissible set theory, and that the other direction is fairly routine.
As it turns out, the exact opposite is the case: the left-to-right direction of the Barwise-Schlipf theorem lends itself to a proof from first principles (as observed independently by Jonathan Stavi and Sol Feferman not long after the appearance of the Barwise-Schmerl paper); and moreover, as recently shown in my joint work with Jim Schmerl, there is a crucial error in the Barwise-Schlipf proof of the right-to-left direction of the theorem, an error that can be circumvented by a rather nontrivial argument. As I will explain, certain results from the joint work of Matt Kaufmann and Jim Schmerl in the mid-1980s on 'lofty' models of arithmetic come in handy for the analysis of the error, and for circumventing it.
- - - - Thursday, May 7, 2020 - - - -
- - - - Friday, May 8, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 8, 2pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Sandra Müller, University of Vienna TBA
- - - - Other Logic News - - - -
A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website, nylogic.github.io, take a look at the following for more seminar listings:
European Set Theory Society
List of upcoming online talks in set theory around the world:
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Wednesday seminar
Prague Set Theory Seminar
4/26/2020 7:35:09
Dear all,
Still no seminars in Prague next week, I am forwarding info about
relevant online seminars and about the PhD thesis defense of Jan Grebik.
The Jerusalem basic concepts seminar will continue on Monday April 27th
at 11 AM Israel time (= 10 AM CEST).
Tsoor Plotnikov will continue the series of talks on Proper forcings and
side conditions.
The Zoom link for the seminar is
Meeting Link:
https://huji.zoom.us/j/99500290990?pwd=K0RYOTVHdlUzd2JURys0RVI3Znd0UT09
Meeting ID: 995 0029 0990
Password: 789132
On Tuesday April 28th at 17:00 Aleksandra Kwiatkowska will give a talk
on "Simplicity of the automorphism groups of homogeneous structures" at
the Wroclaw seminar. If you are interested, ask Piotr Borodulin-Nadzieja
or me for the Zoom link.
The PhD defense of Jan Grebik will take place next Tuesday, May 5th at
10:00 via Zoom, https://cesnet.zoom.us/j/98441831119
The defense is public, guests are welcome and expected. More info here:
https://is.cuni.cz/studium/szz_st/index.php?do=detail_kom&kom=28035&term=587734
Best,
David
On 16/04/2020 12:40, David Chodounsky wrote:
> Dear all,
>
> Still no seminars seminars in Prague in the foreseeable future.
> However, there are interesting set theory online seminar in Jerusalem
> next week, see the forwarded email (note that the times refers to the
> Israel time zone).
>
> Best,
> David
>
>
>
>
> -------- Forwarded Message --------
> Subject: Set Theory seminars next week
> Date: Wed, 15 Apr 2020 20:38:09 +0000
> From: Menachem Magidor
>
>
> The schedule for the set theory seminars (of course via ZOOM) for next
> week is as follows
>
> 1. *The basic learning seminar
> *The seminar will be held on Monday April 20th at 11 am.
> Tsur Plotnikov will start a series of talk about side conditions
> forcing of two types and PFA.
> As introduction the talks will include some basic facts about
> proper forcings.
>
> The Zoom meeting ID for this seminar will be 995 0029 0990 and the
> password is 789132
>
>
> 2. The regular Wednesday seminar will be held on Wednesday April 22nd
> at 11 am.
> Jing Zhang will speak about
> Title: Transformations of the transfinite plane
> Abstract: We discuss the existence of certain transformation functions
> turning pairs of ordinals into triples (or pairs) of ordinals, that
> allows reductions of complicated Ramsey theoretic problems into simpler
> ones. We will focus on the existence of various kinds of strong
> colorings. The basic technique is Todorcevic's walks on ordinals. Joint
> work with Assaf Rinot.
>
> The Zoom meeting ID is 243-676-331
> and no password.
>
> Best
> Menachem Magidor
Wednesday seminar
Prague Set Theory Seminar
4/26/2020 7:35:09
Dear all,
Still no seminars in Prague next week, I am forwarding info about
relevant online seminars and about the PhD thesis defense of Jan Grebik.
The Jerusalem basic concepts seminar will continue on Monday April 27th
at 11 AM Israel time (= 10 AM CEST).
Tsoor Plotnikov will continue the series of talks on Proper forcings and
side conditions.
The Zoom link for the seminar is
Meeting Link:
https://huji.zoom.us/j/99500290990?pwd=K0RYOTVHdlUzd2JURys0RVI3Znd0UT09
Meeting ID: 995 0029 0990
Password: 789132
On Tuesday April 28th at 17:00 Aleksandra Kwiatkowska will give a talk
on "Simplicity of the automorphism groups of homogeneous structures" at
the Wroclaw seminar. If you are interested, ask Piotr Borodulin-Nadzieja
or me for the Zoom link.
The PhD defense of Jan Grebik will take place next Tuesday, May 5th at
10:00 via Zoom, https://cesnet.zoom.us/j/98441831119
The defense is public, guests are welcome and expected. More info here:
https://is.cuni.cz/studium/szz_st/index.php?do=detail_kom&kom=28035&term=587734
Best,
David
On 16/04/2020 12:40, David Chodounsky wrote:
> Dear all,
>
> Still no seminars seminars in Prague in the foreseeable future.
> However, there are interesting set theory online seminar in Jerusalem
> next week, see the forwarded email (note that the times refers to the
> Israel time zone).
>
> Best,
> David
>
>
>
>
> -------- Forwarded Message --------
> Subject: Set Theory seminars next week
> Date: Wed, 15 Apr 2020 20:38:09 +0000
> From: Menachem Magidor
>
>
> The schedule for the set theory seminars (of course via ZOOM) for next
> week is as follows
>
> 1. *The basic learning seminar
> *The seminar will be held on Monday April 20th at 11 am.
> Tsur Plotnikov will start a series of talk about side conditions
> forcing of two types and PFA.
> As introduction the talks will include some basic facts about
> proper forcings.
>
> The Zoom meeting ID for this seminar will be 995 0029 0990 and the
> password is 789132
>
>
> 2. The regular Wednesday seminar will be held on Wednesday April 22nd
> at 11 am.
> Jing Zhang will speak about
> Title: Transformations of the transfinite plane
> Abstract: We discuss the existence of certain transformation functions
> turning pairs of ordinals into triples (or pairs) of ordinals, that
> allows reductions of complicated Ramsey theoretic problems into simpler
> ones. We will focus on the existence of various kinds of strong
> colorings. The basic technique is Todorcevic's walks on ordinals. Joint
> work with Assaf Rinot.
>
> The Zoom meeting ID is 243-676-331
> and no password.
>
> Best
> Menachem Magidor
Set theory seminar this week: Todd Eisworth
Toronto Set Theory Seminar
4/21/2020 13:36:18
Hi everyone,
This Friday, Todd Eisworth (Ohio University) will speak in the seminar on "Representability and pseudopowers."
Abstract: We will prove some basic facts about Shelah’s pseudopower function, and derive some new (?) ZFC results in cardinal arithmetic using basic topological ideas. This talk is designed to be an introduction to this part of pcf theory.
A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website, nylogic.github.io, take a look at the following for more seminar listings:
European Set Theory Society
List of upcoming online talks in set theory around the world:
Recall that given a complete theory TT and a type p(x)p(x) the Hanf number forp(x)p(x) is the least cardinal κκ so that any model of TT of size κκ realizes p(x)p(x) (if such a κκ exists and ∞∞ otherwise). The Hanf number forTT, denoted H(T)H(T), is the supremum of the successors of the Hanf numbers for all possible types p(x)p(x) whose Hanf numbers are <∞<∞. We have seen so far in the seminar that for any complete, consistent TT in a countable language H(T)≤ℶω1H(T)≤ℶω1 (a result due to Morley). In this talk I will present the following theorems: (1) The Hanf number for true arithmetic is ℶωℶω (Abrahamson-Harrington-Knight) but (2) the Hanf number for False Arithmetic is ℶω1ℶω1 (Abrahamson-Harrington)
- - - - Thursday, Apr 23, 2020 - - - -
- - - - Friday, Apr 24, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, April 24, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Arthur Apter, CUNY
Indestructibility and the First Two Strongly Compact Cardinals
Starting from a model of ZFC with two supercompact cardinals, I will discuss how to force and construct a model in which the first two strongly compact cardinals κ1κ1 and κ2κ2 are also the first two measurable cardinals. In this model, κ1κ1's strong compactness is indestructible under arbitrary κ1κ1-directed closed forcing, and κ2κ2's strong compactness is indestructible under Add(κ2,λ)Add(κ2,λ) for any ordinal λλ. This answers a generalized version of a question of Sargsyan.
Next Week in Logic at CUNY:
- - - - Monday, Apr 27, 2020 - - - -
- - - - Tuesday, Apr 28, 2020 - - - -
- - - - Wednesday, Apr 29, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, April 29, 7:00pm
The seminar will take place virtually at 7pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
April 29 Ali Enayat, University of Gothenburg The Barwise-Schlipf characterization of recursive saturation of models of PA
The subject of this talk is a 1975 Barwise-Schlipf landmark paper, whose main theorem asserts that a nonstandard model M of PA is recursively saturated iff M has an expansion to a model of the subsystem Δ11−CA0Δ11−CA0 of second order arithmetic. The impression one gets from reading the Barwise-Schlipf paper is that the left-to-right direction of the theorem is deep since it relies on sophisticated techniques from admissible set theory, and that the other direction is fairly routine.
As it turns out, the exact opposite is the case: the left-to-right direction of the Barwise-Schlipf theorem lends itself to a proof from first principles (as observed independently by Jonathan Stavi and Sol Feferman not long after the appearance of the Barwise-Schmerl paper); and moreover, as recently shown in my joint work with Jim Schmerl, there is a crucial error in the Barwise-Schlipf proof of the right-to-left direction of the theorem, an error that can be circumvented by a rather nontrivial argument. As I will explain, certain results from the joint work of Matt Kaufmann and Jim Schmerl in the mid-1980s on 'lofty' models of arithmetic come in handy for the analysis of the error, and for circumventing it.
- - - - Thursday, Apr 30, 2020 - - - -
- - - - Friday, May 1, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 1, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Joan Bagaria Universitat de Barcelona TBA
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Wednesday seminar
Prague Set Theory Seminar
4/16/2020 6:40:24
Dear all,
Still no seminars seminars in Prague in the foreseeable future.
However, there are interesting set theory online seminar in Jerusalem
next week, see the forwarded email (note that the times refers to the
Israel time zone).
Best,
David
-------- Forwarded Message --------
Subject: Set Theory seminars next week
Date: Wed, 15 Apr 2020 20:38:09 +0000
From: Menachem Magidor
The schedule for the set theory seminars (of course via ZOOM) for next
week is as follows
1. *The basic learning seminar
*The seminar will be held on Monday April 20th at 11 am.
Tsur Plotnikov will start a series of talk about side conditions
forcing of two types and PFA.
As introduction the talks will include some basic facts about
proper forcings.
The Zoom meeting ID for this seminar will be 995 0029 0990 and the
password is 789132
2. The regular Wednesday seminar will be held on Wednesday April 22nd
at 11 am.
Jing Zhang will speak about
Title: Transformations of the transfinite plane
Abstract: We discuss the existence of certain transformation functions
turning pairs of ordinals into triples (or pairs) of ordinals, that
allows reductions of complicated Ramsey theoretic problems into simpler
ones. We will focus on the existence of various kinds of strong
colorings. The basic technique is Todorcevic's walks on ordinals. Joint
work with Assaf Rinot.
The Zoom meeting ID is 243-676-331
and no password.
Best
Menachem Magidor
Wednesday seminar
Prague Set Theory Seminar
4/16/2020 6:40:24
Dear all,
Still no seminars seminars in Prague in the foreseeable future.
However, there are interesting set theory online seminar in Jerusalem
next week, see the forwarded email (note that the times refers to the
Israel time zone).
Best,
David
-------- Forwarded Message --------
Subject: Set Theory seminars next week
Date: Wed, 15 Apr 2020 20:38:09 +0000
From: Menachem Magidor
The schedule for the set theory seminars (of course via ZOOM) for next
week is as follows
1. *The basic learning seminar
*The seminar will be held on Monday April 20th at 11 am.
Tsur Plotnikov will start a series of talk about side conditions
forcing of two types and PFA.
As introduction the talks will include some basic facts about
proper forcings.
The Zoom meeting ID for this seminar will be 995 0029 0990 and the
password is 789132
2. The regular Wednesday seminar will be held on Wednesday April 22nd
at 11 am.
Jing Zhang will speak about
Title: Transformations of the transfinite plane
Abstract: We discuss the existence of certain transformation functions
turning pairs of ordinals into triples (or pairs) of ordinals, that
allows reductions of complicated Ramsey theoretic problems into simpler
ones. We will focus on the existence of various kinds of strong
colorings. The basic technique is Todorcevic's walks on ordinals. Joint
work with Assaf Rinot.
The Zoom meeting ID is 243-676-331
and no password.
Best
Menachem Magidor
Set theory seminar this week: Matteo Viale
Toronto Set Theory Seminar
4/14/2020 8:00:00
Hi everyone,
This Friday, Matteo Viale (University of Torino) will speak in the seminar. His talk is entitled "Tameness for set theory."
Abstract: We show that (assuming large cardinals) set theory is a tractable (and we dare to say tame) first order theory when formalized in a first order signature with natural predicate symbols for the basic definable concepts of second and third order arithmetic, and appealing to the model-theoretic notions of model completeness and model companionship.
Specifically we develop a general framework linking generic absoluteness results to model companionship and show that (with the required care in details) a -property formalized in an appropriate language for second or third order number theory is forcible from some T extending ZFC + large cardinals if and only if it is consistent with the universal fragment of T if and only if it is realized in the model companion of T.
Part (but not all) of our results are conditional to the proof of Schindler and Asperò that Woodin’s axiom (*) can be forced by a stationary set preserving forcing.
I'm very pleased to announce that some seminars are continuing virtually during this turbulent time. Regular weekly mailings of "This Week in Logic" will resume until further notice!
Best regards,
Jonas
This Week in Logic at CUNY:
- - - - Monday, Apr 13, 2020 - - - -
- - - - Tuesday, Apr 14, 2020 - - - -
- - - - Wednesday, Apr 15, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, April 15, 7:00pm
The seminar will take place virtually at 7pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Wei Wang, Institute of Logic and Cognition, Sun Yat-sen University Non-standard models of arithmetic and their standard systems
PA is the first order fragment of Peano's axiomatization of the natural numbers. The natural numbers, N, is called the standard model of PA. But by compactness theorem in first order logic, there are also models of PA different from N, which are called non-standard models of arithmetic. Like in N, every element of a non-standard model M has a binary expansion, which can be regarded as the characteristic function of a subset of N. The standard system of M is the collection of all such subsets of N. It is known that standard systems of non-standard models are always Scott sets and every Scott set of cardinality less than or equal to the first uncountable cardinal is the standard system of some non-standard model. However, the general Scott set problem, whether every Scott set is the standard system of some non-standard model, remains one of the major open problems in the model theory of arithmetic. This talk will present some history of Scott set problem, as well as two constructions of non-standard models with uncountable standard systems.
- - - - Thursday, Apr 16, 2020 - - - -
- - - - Friday, Apr 17, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, April 17, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Corey Switzer, CUNY Specializing Wide Trees Without Adding Reals
An important advancement in iterated forcing was Jensen’s proof that CH does not imply ♢♢ by iteratively specializing Aronszajn trees with countable levels without adding reals thus producing a model of CH plus 'all Aronszajn trees are special'. This proof was improved by Shelah who developed a general method around the notion of dee-complete forcing. This class (under certain circumstances) can be iterated with countable support and does not add reals. However, neither Jensen's nor Shelah's posets will specialize trees of uncountable width and it remains unclear when one can iteratively specialize wider trees. Indeed a very intriguing example, due to Todorčević, shows that there is always a wide Aronszajn tree which cannot be specialized without adding reals. By contrast the ccc forcing for specializing Aronszajn trees makes no distinction between trees of different widths (but may add many reals). In this talk we will provide a general criteria a wide trees Aronszajn tree can have that implies the existence of a dee-complete poset specializing it. Time permitting we will discuss applications of this forcing to forcing axioms compatible with CH and some open questions related to set theory of the reals.
Next Week in Logic at CUNY:
- - - - Monday, Apr 20, 2020 - - - -
- - - - Tuesday, Apr 21, 2020 - - - -
- - - - Wednesday, Apr 22, 2020 - - - -
- - - - Thursday, Apr 23, 2020 - - - -
- - - - Friday, Apr 24, 2020 - - - -
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Set theory seminar this week: Keegan Dasilva Barbosa
Toronto Set Theory Seminar
4/7/2020 8:00:00
Hi everyone,
This Friday, Keegan Dasilva Barbosa will speak on A Decomposition Theorem for Aronszajn Lines.
Abstract: We will prove that under the proper forcing axiom, the class of all Aronszajn lines behave like -scattered orders under the embeddability relation. In particular, we show that the class of better quasi order labeled fragmented Aronszajn lines is itself a better quasi order. Moreover, we show that every better quasi order labeled Aronszajn line can be expressed as a finite sum of labeled types which are algebraically indecomposable. By encoding lines with finite labeled trees, we are also able to deduce a decomposition result, that for every Aronszajn line , there is an such that for any finite colouring of , there is a subset of isomorphic to which uses no more than colours.
The talk will take place this Friday, April 10, from 1:30-3:00 pm EDT on Zoom, details below:
Topic: Set Theory Seminar Time: Apr 10, 2020 01:30 PM Eastern Time (US and Canada)
19:30 CEST (Central Europe)
01:30 AM SST (Singapore)
Bill Chen
Logic Seminar Wed 8 April 2020 17:00 hrs at NUS via Zoom
NUS Logic Seminar
4/2/2020 23:49:27
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 8 April 2020, 17:00 hrs
Zoom: Meeting URL is https://nus-sg.zoom.us/j/786053022 and
Meeting ID is 786 053 022.
Host: Frank Stephan, Department of Mathematics, NUS
Speaker: Wu Guohua.
Title: Members of thin Pi01 classes and their Turing degrees
Abstract: Martin and Pour-El constructed in 1970 a consistent r.e.
theory with few r.e. extensions. Motivated by this work, Cenzer,
Downey, Jockusch and Shore raised the notion of thin Pi01 classes in
their paper in 1993, where a Pi01 class P is thin if every Pi01
subclass of P is the intersection of P and some clopen set. While they
put focus on various Turing degrees of members in these classes, they
also constructed degrees below 0', one r.e., and one minimal,
containing no members of any thin Pi01 classes. In this talk, I will
present basic ideas of the constructions and provide some recent
progress along this topic.
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Set theory seminar this Friday: Iván Ongay Valverde
Toronto Set Theory Seminar
3/31/2020 16:14:47
Hi everyone,
Our seminar returns to break up your social isolation. This week, Iván Ongay Valverde from the University of Wisconsin will speak about Splitting localization and prediction numbers.
Abstract: In 1993, Newelski and Roslanowski studied some cardinal characteristics related to the unsymmetric game (I, as Geschke, called them the localization numbers). While doing this, they found the n-localization property. When a forcing has this property, you can ensure that all new reals are 'tame' somehow (for example, you do not add Cohen or Random reals).
In a different line of study, Andreas Blass worked with some cardinal characteristics related to the idea of guessing correctly a real number given certain amount of information (he called them evasion and prediction numbers). In 2010, it was an open question whether some possible variations of these numbers were known cardinal characteristics or not.
Impressively, these two notions are related.
In this talk, we will show that the k global adaptive prediction numbers are not any other cardinal characteristic. In particular, they are not the localization numbers. To do this, we will use techniques analogue to Newelski and Roslanowski and we will show that the n-localization can be weakened to get their result.
The talk will take place from 1:30-3:00 pm EDT on Zoom, details below.
Bill Chen is inviting you to a scheduled Zoom meeting. Topic: Set Theory Seminar Join Zoom Meeting https://yorku.zoom.us/j/925557716 Meeting ID: 925 557 716
Zoom Address for the Seminar Talk Next Week Wednesday (Logic Seminar NUS)
NUS Logic Seminar
3/28/2020 2:58:16
Dear participants,
The logic seminar will be held as a Zoom Meeting.
In the case that you want to join, please use the following
link on 1 April 2020 a bit before 17:00 hrs Singapore time:
https://nus-sg.zoom.us/j/138746532
Also note that you might need a meeting ID which I forgot in
the previous email. It is ID 138-746-532.
Best regards, Frank Stephan
> ------------------------------------------------------------------------
> Invitation to the Logic Seminar at the National University of Singapore
>
> Date: Wednesday, 1 April 2020, 17:00 hrs (Singapore Time)
>
> Room: S17#04-06, Department of Mathematics, NUS
>
> Speaker: Frank Stephan
>
> Title: Lower Bounds for the Strong N-Conjecture
>
> Abstract:
> The strong n-conjecture is a generalisation of the abc-conjecture
> concerning the limit superior of qualities of n-tuples of integers which
>
> (1) are pairwise co-prime;
>
> (2) have the sum 0;
>
> (3) do not have nontrivial subsums giving 0.
>
> The quality of a tuple is the logarithm of the largest member (by absolute
> value) divided by the logarithm of the largest square-free divider of the
> product of all members of the tuple. Originally it was conjectured that
> the limit superior of these qualities is 1, see the Wikipedia page at
>
> https://en.wikipedia.org/wiki/N_conjecture
>
> but Konyagin (as reported by Browkin 2000) found already an example for
> odd n geq 5 giving the limit superior 3/2; however, Konyagin and Browkin
> did not consider condition (3). The present work reports the following
> main results:
>
> (a) For odd n geq 5, the limit superior is at least 5/3;
>
> (b) For even n geq 6, the limit superior is at least 5/4.
>
> Furthermore, it is shown that for all n geq 6, one can disallow the members
> of the tuple to have any factor from a finite subset F of {3,4,5,...} and
> nevertheless obatin the limit superior 5/4. The last part of the talk reports
> on some analogous result for the Gaussian integers.
>
> Tianyu Liu is writing an UROP about verifying the main claims in the paper
> with the proof assistant COQ and it is planned to work this out to a second
> part of this publication.
>
> This is joint work of Aquinas Hobor, Rupert Hoelzl, Elaine Li, Tianyu Liu
> and Frank Stephan.
>
> Wikipedia Page: https://en.wikipedia.org/wiki/N_conjecture
>
> Paper: https://www.comp.nus.edu.sg/~fstephan/strongnconjecture.pdf
>
> Slides: https://www.comp.nus.edu.sg/~fstephan/strongnconjectureslides.pdf
>
> Seminar Webpage: https://www.comp.nus.edu.sg/~fstephan/logicseminar.html
>
Zoom Address for the Seminar Talk Next Week Wednesday (Logic Seminar NUS)
NUS Logic Seminar
3/27/2020 2:49:42
Dear participants,
The logic seminar will be held as a Zoom Meeting.
In the case that you want to join, please use the following
link on 1 April 2020 a bit before 17:00 hrs Singapore time:
https://nus-sg.zoom.us/j/138746532
Best regards, Frank Stephan
------------------------------------------------------------------------
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 1 April 2020, 17:00 hrs (Singapore Time)
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Frank Stephan
Title: Lower Bounds for the Strong N-Conjecture
Abstract:
The strong n-conjecture is a generalisation of the abc-conjecture
concerning the limit superior of qualities of n-tuples of integers which
(1) are pairwise co-prime;
(2) have the sum 0;
(3) do not have nontrivial subsums giving 0.
The quality of a tuple is the logarithm of the largest member (by absolute
value) divided by the logarithm of the largest square-free divider of the
product of all members of the tuple. Originally it was conjectured that
the limit superior of these qualities is 1, see the Wikipedia page at
https://en.wikipedia.org/wiki/N_conjecture
but Konyagin (as reported by Browkin 2000) found already an example for
odd n geq 5 giving the limit superior 3/2; however, Konyagin and Browkin
did not consider condition (3). The present work reports the following
main results:
(a) For odd n geq 5, the limit superior is at least 5/3;
(b) For even n geq 6, the limit superior is at least 5/4.
Furthermore, it is shown that for all n geq 6, one can disallow the members
of the tuple to have any factor from a finite subset F of {3,4,5,...} and
nevertheless obatin the limit superior 5/4. The last part of the talk reports
on some analogous result for the Gaussian integers.
Tianyu Liu is writing an UROP about verifying the main claims in the paper
with the proof assistant COQ and it is planned to work this out to a second
part of this publication.
This is joint work of Aquinas Hobor, Rupert Hoelzl, Elaine Li, Tianyu Liu
and Frank Stephan.
Wikipedia Page: https://en.wikipedia.org/wiki/N_conjecture
Paper: https://www.comp.nus.edu.sg/~fstephan/strongnconjecture.pdf
Slides: https://www.comp.nus.edu.sg/~fstephan/strongnconjectureslides.pdf
Seminar Webpage: https://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Logic Seminar Talk 1 April 2020 17:00 hrs at NUS
NUS Logic Seminar
3/27/2020 0:52:04
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 1 April 2020, 17:00 hrs (Singapore Time)
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Frank Stephan
Title: Lower Bounds for the Strong N-Conjecture
Abstract:
The strong n-conjecture is a generalisation of the abc-conjecture
concerning the limit superior of qualities of n-tuples of integers which
(1) are pairwise co-prime;
(2) have the sum 0;
(3) do not have nontrivial subsums giving 0.
The quality of a tuple is the logarithm of the largest member (by absolute
value) divided by the logarithm of the largest square-free divider of the
product of all members of the tuple. Originally it was conjectured that
the limit superior of these qualities is 1, see the Wikipedia page at
https://en.wikipedia.org/wiki/N_conjecture
but Konyagin (as reported by Browkin 2000) found already an example for
odd n geq 5 giving the limit superior 3/2; however, Konyagin and Browkin
did not consider condition 3. The present work reports the following
main results:
(a) For odd n geq 5, the limit superior is at least 5/3;
(b) For even n geq 6, the limit superior is at least 5/4.
Furthermore, it is shown that for all n geq 6, one can disallow the members
of the tuple to have any factor from a finite subset F of {3,4,5,...} and
nevertheless obatin the limit superior 5/4. The last part of the talk reports
on some analogous result for the Gaussian integers.
Tianyu Liu is writing an UROP about verifying the main claims in the paper
with the proof assistant COQ and it is planned to work this out to a second
part of this publication.
This is joint work of Aquinas Hobor, Rupert Hoelzl, Elaine Li, Tianyu Liu
and Frank Stephan.
Wikipedia Page: https://en.wikipedia.org/wiki/N_conjecture
Paper: https://www.comp.nus.edu.sg/~fstephan/strongnconjecture.pdf
Slides: https://www.comp.nus.edu.sg/~fstephan/strongnconjectureslides.pdf
Seminar Webpage: https://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Wednesday seminar
Prague Set Theory Seminar
3/26/2020 7:56:04
Dear all,
There is no seminar in Prague next week.
However, people are instead invited to participate the joint Jerusalem
and Bar Ilan set theory seminar which will take place on Wednesday April
1st as an online video conference via Zoom.
Program: Menachem Magidor will speak about the Friedman--Martin theorem
that Borel determinacy can not be proved in Zermelo Set Theory. Namely
one needs reflection for getting it.
The seminar is scheduled to start at 11:00 Israeli time (which should be
10:00 CEST according to my calculations).
The data to joint the video conference:
https://zoom.us/j/243676331
Zoom meeting ID: 243 676 331
Best,
David
Wednesday seminar
Prague Set Theory Seminar
3/23/2020 6:45:19
Dear all,
Because of the current quarantine situation, the Prague Wednesday
seminars are cancelled until further notice.
However, there will be an online seminar (zoom) on Wednesday March 25th
at 9:00--11:00 CET at the Bar-Ilan University, organized by Assaf Rinot.
Menachem Kojman -- Strong colorings over partitions
https://math.biu.ac.il/en/node/864
If you are interested in joining the seminar online, please contact
Assaf Rinot (or me).
Best,
David
Set Theory Seminar this week: Ming Xiao (important meeting information inside!)
Toronto Set Theory Seminar
3/16/2020 10:53:45
Hi everyone,
This week, Ming Xiao will give the seminar. His talk is entitled The Borel chain conditions.
Abstract: In this talk, I will present some examples of Borel posets and show that the hierarchy of partition conditions proposed by Horn and Tarski (-finite chain condition, -bounded chain condition, etc.), when requiring the pieces of partition to be Borel, is still distinct.
IMPORTANT: The seminar will be held remotely using the Zoom software during the usual time, Friday from 1:30 to 3:00 EDT. If you are interested in participating in the seminar and currently NOT a member of the mailing list (e.g., from Set Theory Talks) please send me an email to receive more information about how to join the meeting.
Stay safe,
Bill Chen
Wednesday seminar
Prague Set Theory Seminar
3/16/2020 3:25:18
Dear all,
There is no seminar this week (Wednesday March 18th) due to the quarantine.
The decision and announcement about the next seminar will be made/sent
in about a week.
Best,
David
Logic Seminar 18 March 2020 17:00 hrs at NUS
NUS Logic Seminar
3/14/2020 23:48:12
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 18 March 2020, 17:00 hrs
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Borisa Kuzeljevic.
Title: Cofinal types on the the second uncountable cardinal.
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
In the talk we will present some basic results about the Tukey
ordering of the class of all directed sets whose cofinality is the
second uncountable cardinal. We will isolate some basic directed sets
in this class, and then show which of them have immediate successors
in this ordering.
This is a joint work with Stevo Todorcevic.
This Week in Logic at CUNY
This Week in Logic at CUNY
3/12/2020 22:10:46
Hi everyone,
So far as we know, all seminars are on hiatus for an indefinite period, due to concerns about the covid-19 situation. Regular mailings of This Week in Logic are suspended for the time being, although special announcements will be sent as needed.
Take care of yourselves and each other,
Jonas
Set theory seminar this Friday: Jeffrey Bergfalk
Toronto Set Theory Seminar
3/11/2020 10:34:26
Hi everyone,
This week, Jeffrey Bergfalk from UNAM (Morelia) will speak on Definable (co)homology, topological rigidity, and problems of classification.
Abstract: We describe recent work, joint with Martino Lupini and Aristotelis Panagiotopoulos, at the interface of descriptive set theory and algebraic topology. This work begins with a consideration of the topologies arising naturally in the course of homology and cohomology computations. Our analysis of these topologies has two main benefits:
1. It affords us characterizations of the Borel complexity of several well-studied classification problems in mathematics, and 2. It yields refinements of classical homological and cohomological invariants which are valuable in their own right for the study of topological spaces.
We term the framework of these refined invariants definable (co)homology; this framework amounts to a retention of the descriptive set-theoretic information inhering in algebraic topology computations. These invariants are strong enough to imply several topological rigidity results concerning solenoids (of any dimension) and maps thereon. We will also show that techniques from algebraic topology can, reciprocally, extend the reach of descriptive set theory, by bounding, and in some cases precisely determining, the Borel complexity of classification problems concerning C*- algebras, their automorphisms, or Hermitian line bundles.
The talk will be held on Friday, March 13 in Fields 210 at 1:30 pm. If you will attend, please register using the following link:
Logic and Metaphysics Workshop Date: Monday, March 9, 4.15-6.15 Place: Room 7395, CUNY Graduate Center Antonella Mallozzi (Providence College). Title: Is There an Absolute Modality?
Abstract: Modality seems distinctively pluralistic: there are many kinds of possibility and necessity (logical, physical, metaphysical, normative, etc.), which seem significantly different from one another. However, the various modalities also seem to have much in common–perhaps simply in virtue of being kinds of modality. Should we suppose that there is some fundamental modality, one to which all the other modalities can be somehow reduced? Modal Monism says yes. Particularly, monists may treat the different modalities as relative to some absolute modality. However, Monism, reductionism, and absolute modality need not be a package. Specifically, the claim that some modality is absolute can be understood in ways which are independent of Monism and reductionism. In this talk, I raise concerns for monistic and reductionist programs in modal metaphysics, while also arguing that the notion of absolute modality is ambiguous. Depending on the framework, it means different things and captures quite different desiderata. After exploring several ways of disambiguating it, I suggest that while we possess and deploy a concept of absolute modality, that may be empty; or, otherwise put, no modal truth has the property of being “absolute”. I propose a pluralistic picture that still treats the different modalities as relative, while avoiding both absolute modality and reductionism. Importantly, the proposal won’t impact the philosophical significance of metaphysical modality.
- - - - Tuesday, Mar 10, 2020 - - - -
- - - - Wednesday, Mar 11, 2020 - - - -
The New York City Category Theory Seminar Department of Computer Science, Department of Mathematics The Graduate Center of The City University of New York
Speaker: Tai-Danae Bradley, The Graduate Center, CUNY. Date and Time: Wednesday March 11, 2020, 7:00 - 8:30 PM., Room 6417. Title: Modeling Probability Distributions as Quantum States.
Abstract: This talk features a passage from classical probability to quantum probability. The quantum version of a classical probability distribution is a density operator on a Hilbert space. The quantum version of a marginal probability distribution is a reduced density operator, and the operation that plays the role of marginalization is the partial trace. In particular, every joint probability distribution on a finite set can be modeling as a rank 1 density operator—a pure quantum state. With the partial trace, we recover the classical marginal probabilities, but we also uncover additional information. This extra information can be understood explicitly from the spectral information of the reduced density operators. I’ll describe these ideas and share how they contribute to understanding mathematical structure within natural language.
- - - - Thursday, Mar 12, 2020 - - - -
- - - - Friday, Mar 13, 2020 - - - -
Model Theory Seminar CUNY Graduate Center, Room 6417 Friday, March 13, 12:30-2:00pm
Rebecca Coulson, United States Military Academy TBA
Logic Workshop CUNY Graduate Center, Room 6417 Friday, March 13, 2:00-3:30pm
Chris Conidis, CUNY The complexity of radical constructions in rings and modules
We present two different elementary algebraic constructions that are as complicated as possible and whose complexity vastly exceeds those typically found in the elementary algebra literature. The first is the prime radical of a noncommutative ring, while the second is the radical of a module. These constructions contrast similar constructions in more familiar contexts that we will also mention along the way. We will spend most of our time describing how to construct radicals that are as complicated as possible from a computability point of view.
Next Week in Logic at CUNY:
- - - - Monday, Mar 16, 2020 - - - -
Logic and Metaphysics Workshop Date: Monday, March 16, 4.15-6.15 Place: Room 7395, CUNY Graduate Center
David Papineau (CUNY) Title: The Statistical Nature of Causation
Abstract: For over a hundred years econometricians, epidemiologists, educational sociologists and other non-experimental scientists have used asymmetric correlational patterns to infer directed causal structures. It is odd, to say the least, that no philosophical theories of causation cast any light on why these techniques work. Why do the directed causal structures line up with the asymmetric correlational patterns? Judea Pearl says that the correspondence is a “gift from the gods”. Metaphysics owes us a better answer. I shall attempt to sketch the outline of one.
- - - - Tuesday, Mar 17, 2020 - - - -
- - - - Wednesday, Mar 18, 2020 - - - -
- - - - Thursday, Mar 19, 2020 - - - -
- - - - Friday, Mar 20, 2020 - - - -
Ad Hoc Workshop on the Semantic Paradoxes When? Friday March 20, Noon-5pm Where? CUNY Graduate Center, room TBA Who? Will Nava, NYU, ‘Expressability and the (Un)Paradoxicality Paradoxes’ Brian Porter, GC, ‘Paraconsistent and Paracomplete Solutions to the Validity Curry Paradox’ Chris Scambler, NYU, ‘Metainferences and Paradox’ Open to? All interested Queries? Graham Priest, priest.graham@gmail.com The workshop is sponsored by the Kripke Center.
- - - - Other Logic News - - - -
MAMLS Spring Fling This is a three day conference (April 22-24) in the mathematical field of set theory to be held at the CUNY Graduate Center. Consult the website (https://nylogic.github.io/MAMLSSpringFling/home.html) for more details.
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
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Logic Seminar Wed 11 March 2020 17:00 hrs at NUS by Thilo Weinert
NUS Logic Seminar
3/8/2020 18:24:12
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 11 March 2020, 17:00 hrs
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Thilo Weinert, NUS
Title: Polarised partition relation for order types
URL: https://arxiv.org/abs/1810.13316
and https://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
We analyse partitions of products with two ordered factors in two
classes where both factors are countable or well-ordered and at least
one of them is countable. This relates the partition properties of
these products to cardinal characteristics of the continuum. We build
on work by Erdoes, Garti, Jones, Orr, Rado, Shelah and
Szemeredi. In particular, we show that a theorem of Jones
extends from the natural numbers to the rational ones but consistently
extends only to three further equimorphism classes of countable
orderings. This is made possible by applying a thirteen-year old
theorem of Orr about embedding a given order into a sum of finite
orders indexed over the given order.
This is joint work with Lukas Klausner
Fulgencio Lopez, Uncountable equilateral sets and anti-Ramsey families of functions.
IMPAN Working Group in Applications of Set Theory
3/7/2020 13:45:59
Seminar: Working group in applications of set theory, IMPAN
Tuesday, 10.03.2020, 10:15 pm, room 105, IMPAN, Śniadeckich 8, Warsaw.
Speaker: Fulgencio Lopez (IMPAN)
Title: "Uncountable equilateral sets and anti-Ramsey families of functions."
Abstact: "The study of equilateral and separated sets in Banach spaces has been an active area of interest since Petty considered this question in non euclidean spaces in 1971. We will give some background results in the area and then focus on the case of spaces of continuous functions. In particular we will show that having an anti-Ramsey family of functions implies there is a compact connected K, such that its space of continuous functions has no uncountable equilateral sets. A known result says that the existence of uncountable equilateral sets in all nonseparable C(K) spaces is undecidable." (joint work with P. Koszmider)
Visit our seminar webpage which may include announcements of some future talks at https://www.impan.pl/~set_theory/Seminar/
Cheers, Piotr.
Set theory seminar this Friday
Toronto Set Theory Seminar
3/4/2020 11:12:37
Hi everyone,
Hossein will speak in the seminar this week. His talk is entitled Rigidity of Souslin trees and .
Abstract:
We will show that is consistent with the statement there is no minimal Souslin tree. This answers a question due to Baumgartner. We will also show that there is a Souslin tree whose restriction on any is rigid and forcing with makes a Kurepa tree. This answers a question due to Gunter Fuchs.
The talk will be held on Friday, March 6 in Fields 210 at 1:30 pm. The talk is expected to be short, probably less than an hour in duration. If you will attend, please register using the following link:
Logic and Metaphysics Workshop Date: Monday, March 2, 4.15-6.15 Place: Room 7395, CUNY Graduate Center
Alex Citkin (Metropolitan Telecommunications). Title: Deductive Systems with Unified Multiple-Conclusion Rules
Abstract: Some people fight for the rights of animals, I am fighting for the rights of rejected propositions. Following the approach suggested by Brentano and accepted and developed by Lukasiewicz, I study the deductive systems that treat asserted and rejected propositions equally, in the same way. By “statement,” we understand the expressions of form +A – “A being asserted”, and -A$ – “A being rejected”, where A is a proposition. Accordingly, by a “unified logic,” we understand a consequence relation between sets of statements and statements. We introduce the unified deductive systems which can be used to define the unified logics. Unified deductive system consists of axioms, anti-axioms, and the multiple conclusion inference rules which premises and conclusions are the statements rather than the propositions. In particular, we study the deductive systems that contain the coherency rule, which means that one cannot assert and reject the same proposition at the same time, and the fullness rule, which means that each proposition is either asserted or rejected. Inclusion of these rules though does not enforce the law of excluded middle, or the law of non-contradiction on the propositional level.
- - - - Tuesday, Mar 3, 2020 - - - -
- - - - Wednesday, Mar 4, 2020 - - - -
The New York City Category Theory Seminar Department of Computer Science, Department of Mathematics The Graduate Center of The City University of New York
Speaker: Noah Chrein, University of Maryland. Date and Time: Wednesday March 4, 2020, 7:00 - 8:30 PM., Room 6417. Title: Hierarchy and Anisotropy in Categorical Ontology.
Abstract: The theory of sheaves on a site allows us to break down objects into local pieces and recover data about the global object. We wish to treat systems outside of mathematics in the same way: by breaking down objects into local pieces, analyzing the local pieces, and recombining to get an analysis of the whole. When running a simulation, it's not always relevant to understand the atoms of every object, sometimes it is enough to understand objects abstractly, this is the concept of "anisotropy". We propose a modeling scheme that follows the development of sheaf theory, and adds a notion of hierarchical anisotropy. Namely, instead of a covering in a site, {U_i -> X}, we will treat the U_i and X in two different categories, with "Ontological Expansions" O(X) = {U_i}. In this way, we can decide to treat objects globally, or if we need more specific information, we can expand into local pieces. To this end we define a Hierarchical Ontology.
- - - - Thursday, Mar 5, 2020 - - - -
- - - - Friday, Mar 6, 2020 - - - -
Model Theory Seminar CUNY Graduate Center, Room 6417 Friday, March 6, 12:30-2:00pm
Dave Marker, McMaster University Computability of the countable saturated differentially closed field
It's been known since work of Harrington in the early 1970s that computable differential fields have computable differential closures. Recently Calvert, Frolov, Harizanov, Knight, McCoy, Soskova, and Vatev showed that the countable saturated differentially closed field is computable. Their proof involves first creating an effective listing of all types and then using a result of Morley's on existence of computable saturated models. I will give a significant simplification of the enumeration result and, for completeness, sketch Morley's priority construction of a saturated model. Pillay has also given an alternative enumeration argument though ours seems more robust and generalizes to quantifier free types in ACFA.
Logic Workshop CUNY Graduate Center, Room 6417 Friday, March 6, 2:00-3:30pm Johanna Franklin, Hofstra University Lowness for isomorphism and Turing degrees
A Turing degree is low for isomorphism if whenever it can compute an isomorphism between two countably presented structures, there is already a computable isomorphism between them and thus there is no need to use the degree as an oracle at all. I will discuss the types of degrees that are low for isomorphism and the extent to which this class of degrees has the same properties as other lowness classes.
This work is joint with Reed Solomon.
Next Week in Logic at CUNY:
- - - - Monday, Mar 9, 2020 - - - -
Logic and Metaphysics Workshop Date: Monday, March 9, 4.15-6.15 Place: Room 7395, CUNY Graduate Center Alex Citkin (Metropolitan Telecommunications). Title: Deductive Systems with Unified Multiple-Conclusion Rules
Abstract: Some people fight for the rights of animals, I am fighting for the rights of rejected propositions. Following the approach suggested by Brentano and accepted and developed by Lukasiewicz, I study the deductive systems that treat asserted and rejected propositions equally, in the same way. By “statement,” we understand the expressions of form +A – “A being asserted”, and -A$ – “A being rejected”, where A is a proposition. Accordingly, by a “unified logic,” we understand a consequence relation between sets of statements and statements. We introduce the unified deductive systems which can be used to define the unified logics. Unified deductive system consists of axioms, anti-axioms, and the multiple conclusion inference rules which premises and conclusions are the statements rather than the propositions. In particular, we study the deductive systems that contain the coherency rule, which means that one cannot assert and reject the same proposition at the same time, and the fullness rule, which means that each proposition is either asserted or rejected. Inclusion of these rules though does not enforce the law of excluded middle, or the law of non-contradiction on the propositional level.
- - - - Tuesday, Mar 10, 2020 - - - -
- - - - Wednesday, Mar 11, 2020 - - - -
The New York City Category Theory Seminar Department of Computer Science, Department of Mathematics The Graduate Center of The City University of New York
Speaker: Tai-Danae Bradley, The Graduate Center, CUNY. Date and Time: Wednesday March 11, 2020, 7:00 - 8:30 PM., Room 6417. Title: Modeling Probability Distributions as Quantum States.
Abstract: This talk features a passage from classical probability to quantum probability. The quantum version of a classical probability distribution is a density operator on a Hilbert space. The quantum version of a marginal probability distribution is a reduced density operator, and the operation that plays the role of marginalization is the partial trace. In particular, every joint probability distribution on a finite set can be modeling as a rank 1 density operator—a pure quantum state. With the partial trace, we recover the classical marginal probabilities, but we also uncover additional information. This extra information can be understood explicitly from the spectral information of the reduced density operators. I’ll describe these ideas and share how they contribute to understanding mathematical structure within natural language.
- - - - Thursday, Mar 12, 2020 - - - -
- - - - Friday, Mar 13, 2020 - - - -
Logic Workshop CUNY Graduate Center, Room 6417 Friday, March 13, 2:00-3:30pm
Chris Conidis, CUNY TBA
- - - - Other Logic News - - - -
CONFERENCE ANNOUNCEMENT:
We are pleased to announce that the 2020 Boise Extravaganza in Set Theory (BEST) conference will take place in Ashland, Oregon, on the campus of Southern Oregon University, June 17–18, 2020.
https://www.boisestate.edu/math/best/ BEST is an international conference featuring talks on a broad range of recent advances in research in set theory, logic, and related fields. Researchers from all areas of set theory and logic are welcome. BEST particularly aims to support the careers of young researchers. The conference is organized by the Set Theory and Logic group at Boise State University and is structured as a symposium of the annual meeting of the AAAS, Pacific Division.
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
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Wednesday seminar
Prague Set Theory Seminar
2/29/2020 10:58:52
Dear all,
There will be no seminar on Wednesday for the next two weeks (regular
participants are unavailable). The seminar should meet again on
Wednesday March 18th.
Best,
David
Tomasz Kochanek, On representations of the Calkin algebra - the noncommutative analogue of P(N)/Fin or l∞/c0 II
IMPAN Working Group in Applications of Set Theory
2/29/2020 9:01:08
Seminar: Working group in applications of set theory, IMPAN
TUESDAY, 3.03.2020,
Seminar at 10:15 pm, room 105, IMPAN, Śniadeckich 8, Warsaw.
Speaker: Tomasz Kochanek (IM PAN/MIM UW)
Title: " On representations of the Calkin algebra - the noncommutative analogue of P(N)/Fin or l∞/c0 II "
Abstact: "Continuing our study of the poset of projections of the Calkin algebra Q(H), we will first show that below any strictly decreasing sequence of projections of Q(H) there is some nonzero projection. This fact gives rise to considering a `quantized` analogue of the pseudointersection number. Next, we will prove a general result saying that the poset of projections of Q(A) does not form a lattice, whenever Q(A) is the corona algebra of any stabilization A of some unital C*-algebra. In particular, this implies that the Calkin algebra is not an AW*-algebra. Then, we will proceed to the problem of representation of Q(H), focusing on two papers. First, Anderson and Bunce (Amer. J. Math. 1977) showed that under Martin's axiom (as well as under the Continuum Hypothesis), there exists a faithful *-representation of Q(H) such that the WOT-closure of its range is a II∞ type factor. Later, Anderson (J. Funct. Anal. 1979) showed that such a result holds true in ZFC. We shall discuss both of those (quite similar) constructions.".
Visit our seminar webpage which may include announcements of some future talks at https://www.impan.pl/~set_theory/Seminar/
Cheers, Piotr.
(KGRC) research seminar talk on Thursday, March 5
Kurt Godel Research Center
2/27/2020 15:32:02
The KGRC welcomes as guests:
Jana Marikova (host: Benjamin Miller) will stay until June 30.
Clifton Ealy (host: Benjamin Miller) will visit from March 7 to March 15 and
from May 9 to June 30.
Miguel Moreno (host: Lyubomyr Zdomskyy) will stay until November 30 and give a
talk on January 23.
Jerzy Kakol (host: Damian Sobota) will stay from March 29 to April 4 and give a
talk on April 2.
Chi Tat Chong (host: Sy-David Friedman) will stay from June 17 to June 19 and
give a talk on June 18.
(Note: Professor Zeman's visit in the first week of March had to be canceled.)
* * *
Research seminar
Kurt Gödel Research Center
Thursday, March 5
"$\Pi_1^1$-subcompactness and type omission"
Yair Hayut (KGRC)
Strongly compact cardinals can be characterized in various ways: compactness of
$L_{\kappa,\kappa}$, filter extensions, the existence of fine measures, the
strong tree property (+inaccessibility) and many other ways. Localizations of
those definitions produce a rich hierarchy. Supercompact cardinals have much
fewer parallel characterizations, obtained typically by adding a normality
assumption.
In this talk I will present a characterization of supercompact cardinals in
terms of compactness of $L_{\kappa,\kappa}$ with type omission. Using it, I
will present a variant of the strong tree property which is (locally) weaker
than the ineffable tree property and together with inaccessibility characterize
supercompactness. Those characterizations localize to a characterization of
$\Pi^1_1$-subcomapctness.
This is a joint work with Menachem Magidor.
Time and Place
Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47)
Talk at 4:00pm in the KGRC lecture room (seminar room D5.48)
Universität Wien
Institut für Mathematik
Kurt Gödel Research Center
Augasse 2-6, UZA 1 - Building 2
1090 Wien
Set Theory Seminar this Friday
Toronto Set Theory Seminar
2/26/2020 11:38:54
We will continue with the second part of the talk this Friday, February 28 in Fields 210 from 1:30 to 3:00. If you will attend the talk, please register using the following link:
On Wed, Feb 12, 2020 at 10:00 AM Bill Chen <chenwb@gmail.com> wrote:
Hi everyone,
I will talk this week about selectivity properties of spaces.
Abstract: This talk addresses several questions of Feng, Gruenhage, and Shen which arose from Michael's theory of continuous selections from countable spaces. This theory is concerned with the following general question about topological spaces: when does a map from into the hyperspace of closed nonempty subsets of admit a continuous selection ?
We construct a space which is -selective but not -selective from , and an -selective space which is not selective for a -point ultrafilter from CH. We also produce ZFC examples of Fréchet spaces where countable subsets are first countable which are not -selective. All of the notions will be defined in the talk, joint work with Paul Szeptycki.
The talk will be held at the usual time and place on Friday, February 14 in Fields 210 from 1:30 to 3:00. If you will attend the talk, please register using the following link:
Fernando Javier Núñez Rosales: Teoría descriptiva de grupos polacos no arquimedianos de transformaciones
Mexico City Logic Seminar
2/25/2020 11:52:00
Los grupos polacos no arquimedianos se pueden realizar como grupos de automorfismos de estructuras de Fraïssé. El objetivo de esta plática es revisar algunos fenómenos de la dinámica de estos grupos, los cuales pueden ser estudiados a través de propiedades combinatorias de clases de estructuras finitas o sistemas asociados a estas vía teoría de Fraïssé. Algunos de los tópicos centrales serán la extrema promediabilidad; el cómputo de flujos minimales universales; la existencia de simetrías genéricas y de genéricos enormes; aproximación por compactos; turbulencia; entre otras. Estos tópicos serán ilustrados con ejemplos.
Tagged: Fernando Javier Núñez Rosales
Logic Seminar 4 March 2020 17:00 hrs at NUS by Andre Nies
NUS Logic Seminar
2/24/2020 21:20:21
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 4 March 2019, 17:00 hrs
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Andre Nies, University of Auckland
Title: Analogs of combinatorial cardinal characteristics in
computability theory
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
Our basic objects are infinite sets of natural numbers. In set theory,
the MAD number is the least cardinality of a maximal almost disjoint
class of sets of natural numbers. The ultrafilter number is the least
size of an ultrafilter base.
We study computability theoretic analogs of these cardinals. In our
approach, all the basic objects will be infinite computable sets. A
class of such basic objects is encoded as the set of columns of a set
R, which allows us to study the Turing complexity of the class.
We show that each non-low oracle computes a MAD class R, give a
finitary construction of a c.e. MAD set (compatible with permitting),
and on the other hand show that a 1-generic below the halting problem
does not compute a MAD class.
We show that the Turing degrees of ultrafilter bases are precisely the
high degrees.
Joint work with: Steffen Lempp, Joseph S. Miller and Mariya Soskova
Reference: Section 8 of Logic Blog 2019 on Andre's homepage; soon also
available as technical report on http://www.arxiv.org/.
SPECIAL ANNOUNCEMENT - This Week in Logic at CUNY - Two add'l talks today
This Week in Logic at CUNY
2/24/2020 12:35:59
Hi everyone,
Please see the announcement below, provided by Dennis Sullivan.
Best,
Jonas
---------------------------------
Prof. Francisco Javier Torres de Lizaur from Spain will give two talks today at the Einstein Chair seminar today, February 24, 2020:
The first will relate to geometry.
The second will relate to 3D fluid solutions in space to logic, computer science and PDE.
Namely, at 4:00p in logic knowing if a point enters a region contains the halting problem.
This affects PDE, analysis and computer science and at 2:00p finding links knots and foliations in stationary solutions of Euler’s fluid PDE in 3D.
<2:00p to tea then 4:00 to 5:00p>
<ROOM 6417>
This Week in Logic at CUNY
This Week in Logic at CUNY
2/23/2020 20:33:37
This Week in Logic at CUNY:
- - - - Monday, Feb 24, 2020 - - - -
Logic and Metaphysics Workshop Date: Monday, February 24, 4.15-6.15 Place: Room 7395, CUNY Graduate Center Dongwoo Kim (CUNY) Title: A Truthmaker Semantics for Modal Logics
Abstract: This paper attempts to provide an exact truthmaker semantics for a family of normal modal propositional logic. The new semantics can be regarded as an “exactification” of the Kripke semantics in the sense of Fine (2014). For it offers an account of the accessibility relation on worlds in terms of the banning and allowing relations on states. The main idea is that an exact truthmaker for “Necessarily P” is a state that bans the exact falsifiers of P from obtaining, and an exact truthmaker for “Possibly P” is a state that allows the exact verifiers of P to obtain.
- - - - Tuesday, Feb 25, 2020 - - - -
- - - - Wednesday, Feb 26, 2020 - - - -
The New York City Category Theory Seminar Department of Computer Science, Department of Mathematics The Graduate Center of The City University of New York Speaker: Noson S. Yanofsky, Brooklyn College, CUNY. Date and Time: Wednesday February 26, 2020, 7:00 - 8:30 PM., Room 6417.
Title: Higher-Order Categorical Logic: From Section 1.7 and on.
Abstract: We will be talking about Polynomial categories and Kleisli categories of cotriples. We will also talk about coproducts in Cartesian closed categories and natural number objects.
- - - - Thursday, Feb 27, 2020 - - - -
- - - - Friday, Feb 28, 2020 - - - -
Logic Workshop CUNY Graduate Center, Room 6417 Friday, February 28, 2:00-3:30pm
Joel Nagloo, CUNY TBA
Next Week in Logic at CUNY:
- - - - Monday, Mar 2, 2020 - - - -
Logic and Metaphysics Workshop Date: Monday, March 2, 4.15-6.15 Place: Room 7395, CUNY Graduate Center
Alex Citkin (Metropolitan Telecommunications). Title: Deductive Systems with Unified Multiple-Conclusion Rules
Abstract: Some people fight for the rights of animals, I am fighting for the rights of rejected propositions. Following the approach suggested by Brentano and accepted and developed by Lukasiewicz, I study the deductive systems that treat asserted and rejected propositions equally, in the same way. By “statement,” we understand the expressions of form +A – “A being asserted”, and -A$ – “A being rejected”, where A is a proposition. Accordingly, by a “unified logic,” we understand a consequence relation between sets of statements and statements. We introduce the unified deductive systems which can be used to define the unified logics. Unified deductive system consists of axioms, anti-axioms, and the multiple conclusion inference rules which premises and conclusions are the statements rather than the propositions. In particular, we study the deductive systems that contain the coherency rule, which means that one cannot assert and reject the same proposition at the same time, and the fullness rule, which means that each proposition is either asserted or rejected. Inclusion of these rules though does not enforce the law of excluded middle, or the law of non-contradiction on the propositional level.
- - - - Tuesday, Mar 3, 2020 - - - -
- - - - Wednesday, Mar 4, 2020 - - - -
The New York City Category Theory Seminar Department of Computer Science, Department of Mathematics The Graduate Center of The City University of New York
Speaker: Noah Chrein, University of Maryland. Date and Time: Wednesday March 4, 2020, 7:00 - 8:30 PM., Room 6417. Title: Hierarchy and Anisotropy in Categorical Ontology.
Abstract: The theory of sheaves on a site allows us to break down objects into local pieces and recover data about the global object. We wish to treat systems outside of mathematics in the same way: by breaking down objects into local pieces, analyzing the local pieces, and recombining to get an analysis of the whole. When running a simulation, it's not always relevant to understand the atoms of every object, sometimes it is enough to understand objects abstractly, this is the concept of "anisotropy". We propose a modeling scheme that follows the development of sheaf theory, and adds a notion of hierarchical anisotropy. Namely, instead of a covering in a site, {U_i -> X}, we will treat the U_i and X in two different categories, with "Ontological Expansions" O(X) = {U_i}. In this way, we can decide to treat objects globally, or if we need more specific information, we can expand into local pieces. To this end we define a Hierarchical Ontology.
- - - - Thursday, Mar 5, 2020 - - - -
- - - - Friday, Mar 6, 2020 - - - -
Logic Workshop CUNY Graduate Center, Room 6417 Friday, March 6, 2:00-3:30pm Johanna Franklin, Hofstra University Lowness for isomorphism and Turing degrees
A Turing degree is low for isomorphism if whenever it can compute an isomorphism between two countably presented structures, there is already a computable isomorphism between them and thus there is no need to use the degree as an oracle at all. I will discuss the types of degrees that are low for isomorphism and the extent to which this class of degrees has the same properties as other lowness classes.
This work is joint with Reed Solomon.
- - - - Other Logic News - - - -
CONFERENCE ANNOUNCEMENT:
We are pleased to announce that the 2020 Boise Extravaganza in Set Theory (BEST) conference will take place in Ashland, Oregon, on the campus of Southern Oregon University, June 17–18, 2020.
https://www.boisestate.edu/math/best/ BEST is an international conference featuring talks on a broad range of recent advances in research in set theory, logic, and related fields. Researchers from all areas of set theory and logic are welcome. BEST particularly aims to support the careers of young researchers. The conference is organized by the Set Theory and Logic group at Boise State University and is structured as a symposium of the annual meeting of the AAAS, Pacific Division.
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
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Tomasz Kochanek, On representations of the Calkin algebra - the noncommutative analogue of P(N)/Fin or l∞/c0
IMPAN Working Group in Applications of Set Theory
2/22/2020 9:39:21
Seminar: Working group in applications of set theory, IMPAN
Note the change from Thursdays to Tuesdays and afternoons to mornings.
TUESDAY, 25.02.2020,
Seminar at 10:15 pm, room 105, IMPAN, Śniadeckich 8, Warsaw.
Speaker: Tomasz Kochanek (IM PAN/MIM UW)
Title: " On representations of the Calkin algebra - the noncommutative analogue of P(N)/Fin or l∞/c0"
Abstact: "The first part will be a mild introduction to the Calkin algebra Q(H) which was first investigated thoroughly by J.W. Calkin in his paper published in Annals Math. in 1941. We shall present some basic facts on Q(H), explaining what it has to do with essential spectra, Fredholm operators, the BDF theory of extensions, and a few other things. With the aid of Banach limit, we will construct a `concrete' representation ρ of Q(H) on a Hilbert space of density continuum. Also, we will show that the range of ρ is not closed in the weak operator topology, which should provoke considering the problem of finding some `special' representations of Q(H), as well as the problem of extending *-homomorphisms into Q(H). This will be the topic of the second part".
Visit our seminar webpage which may include announcements of some future talks at https://www.impan.pl/~set_theory/Seminar/
Cheers, Piotr.
Wednesday seminar
Prague Set Theory Seminar
2/21/2020 12:39:39
Dear all,
The seminar meets on Wednesday February 26th at 11:00 in the Institute
of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Egbert Thümmel will talk about the non-existence of ω1 purely
injective ideals in Boolean algebras.
Best,
David
This Week in Logic at CUNY
This Week in Logic at CUNY
2/18/2020 22:30:32
This Week in Logic at CUNY:
- - - - Monday, Feb 17, 2020 - - - -
- - - - Tuesday, Feb 18, 2020 - - - -
- - - - Wednesday, Feb 19, 2020 - - - -
MOPA (Models of Peano Arithmetic) CUNY Graduate Center, Room 4213.03 (Math Thesis Room) Wednesday, February 19, 6:30-8:00pm
James Geiser Soundness and the Gödel Undecidability Theorem
The goal of Gödel’s argument that the theory (T) of Peano Arithmetic is not complete, was to show that the Gödel sentences, GG , and it’s negation, are not provable in T, unless T is inconsistent. In this paper we examine the first half of this argument, namely, that from a hypothetical derivation, PGPG, of GG, a derivation, PfPf, can be constructed that ends in a contradiction. We make the observation that the Gödel argument depends on the metatheory concept of representability that, in turn, depends on the metatheory concept of soundness. Our analysis leads to two main observations, the first well know, and the second, a challenge to the standard undecidability argument.
1 – The existence of PGPG implies that T is unsound. This conclusion does not require the further construction, from PGPG, of the derivation PfPf.
2 - We argue that effectuation of the construction of PfPf is obstructed, because that effectuation requires acceptance of a contradiction in the metatheory regarding the soundness of T.
This is joint work with Catherine Hennix.
The New York City Category Theory Seminar Department of Computer Science, Department of Mathematics The Graduate Center of The City University of New York Date and Time: Wednesday February 19, 2020, 7:00 - 8:30 PM., Room 6417. Speaker: Todd Trimble, Western Connecticut State University. Title: The Universal Property of the Bar Construction.
Abstract: The bar construction is a fundamental construction used throughout homological algebra and algebraic topology, including for example the construction of classifying bundles, deloopings of suitable H-spaces, and free resolutions of general algebras and the cohomology thereof. The underlying theme is that the bar construction produces canonical contractible or acyclic simplicial algebras, as usually explained by the acyclic models theorem. In this talk we sharpen this result, giving a precise sense in which the bar construction is a universal acyclic simplicial algebra, here recasting "acyclic" not as a property but as an algebraic structure, whereby acyclic structures are coalgebras over the decalage comonad.
- - - - Thursday, Feb 20, 2020 - - - -
- - - - Friday, Feb 21, 2020 - - - -
Logic Workshop CUNY Graduate Center, Room 6417 Friday, February 21, 2:00-3:30pm Andrey Morozov, Novosibirsk State University On ΣΣ-preorderings in HF(R) We prove that ω1ω1 cannot be embedded into any preordering ΣΣ-definable with parameters in the hereditarily finite superstructure over the ordered field of real numbers, HF(R). As corollaries, we obtain characterizations of ΣΣ-presentable ordinals and Gödel constructive sets of kind LαLα. It also follows that there are no ΣΣ-presentations for structures of TT-, mm-, 11-, and tttt-degrees over HF(R).
Next Week in Logic at CUNY:
- - - - Monday, Feb 24, 2020 - - - -
Logic and Metaphysics Workshop Date: Monday, February 24, 4.15-6.15 Place: Room 7395, CUNY Graduate Center Dongwoo Kim (CUNY) Title: A Truthmaker Semantics for Modal Logics
Abstract: This paper attempts to provide an exact truthmaker semantics for a family of normal modal propositional logic. The new semantics can be regarded as an “exactification” of the Kripke semantics in the sense of Fine (2014). For it offers an account of the accessibility relation on worlds in terms of the banning and allowing relations on states. The main idea is that an exact truthmaker for “Necessarily P” is a state that bans the exact falsifiers of P from obtaining, and an exact truthmaker for “Possibly P” is a state that allows the exact verifiers of P to obtain.
- - - - Tuesday, Feb 25, 2020 - - - -
- - - - Wednesday, Feb 26, 2020 - - - -
The New York City Category Theory Seminar Department of Computer Science, Department of Mathematics The Graduate Center of The City University of New York Date and Time: Wednesday February 26, 2020, 7:00 - 8:30 PM., Room 6417.
Title: Higher-Order Categorical Logic: From Section 1.7 and on.
Abstract: We will be talking about Polynomial categories and Kleisli categories of cotriples. We will also talk about coproducts in Cartesian closed categories and natural number objects.
- - - - Thursday, Feb 27, 2020 - - - -
- - - - Friday, Feb 28, 2020 - - - -
Logic Workshop CUNY Graduate Center, Room 6417 Friday, February 28, 2:00-3:30pm
Joel Nagloo, CUNY TBA
- - - - Other Logic News - - - -
CONFERENCE ANNOUNCEMENT:
We are pleased to announce that the 2020 Boise Extravaganza in Set Theory (BEST) conference will take place in Ashland, Oregon, on the campus of Southern Oregon University, June 17–18, 2020.
https://www.boisestate.edu/math/best/ BEST is an international conference featuring talks on a broad range of recent advances in research in set theory, logic, and related fields. Researchers from all areas of set theory and logic are welcome. BEST particularly aims to support the careers of young researchers. The conference is organized by the Set Theory and Logic group at Boise State University and is structured as a symposium of the annual meeting of the AAAS, Pacific Division.
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
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Logic seminar this week cancelled
NUS Logic Seminar
2/18/2020 1:36:05
Hello,
I just want to inform you that our speaker for the logic seminar this
week is ill and on mc until Thursday. Therefore there is no logic seminar
this week. My apologies and all the best wishes to Thilo for his health.
Best regards, Frank
Wednesday seminar
Prague Set Theory Seminar
2/13/2020 6:13:04
Dear all,
There is no seminar next week, Wednesday February 19th.
The seminar should meet again on Wednesday February 26th.
Best,
David
Logic Seminar 19 Feb 2020 17:00 hrs at NUS
NUS Logic Seminar
2/13/2020 2:47:21
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 19 February 2019, 17:00 hrs
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Thilo Weinert, NUS
Title: Polarised partition relation for order types
URL: https://arxiv.org/abs/1810.13316
and https://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
We analyse partitions of products with two ordered factors in two
classes where both factors are countable or well-ordered and at least
one of them is countable. This relates the partition properties of
these products to cardinal characteristics of the continuum. We build
on work by Erdoes, Garti, Jones, Orr, Rado, Shelah and
Szemeredi. In particular, we show that a theorem of Jones
extends from the natural numbers to the rational ones but consistently
extends only to three further equimorphism classes of countable
orderings. This is made possible by applying a thirteen-year old
theorem of Orr about embedding a given order into a sum of finite
orders indexed over the given order.
This is joint work with Lukas Klausner
Set Theory Seminar this Friday
Toronto Set Theory Seminar
2/12/2020 10:00:00
Hi everyone,
I will talk this week about selectivity properties of spaces.
Abstract: This talk addresses several questions of Feng, Gruenhage, and Shen which arose from Michael's theory of continuous selections from countable spaces. This theory is concerned with the following general question about topological spaces: when does a map from into the hyperspace of closed nonempty subsets of admit a continuous selection ?
We construct a space which is -selective but not -selective from , and an -selective space which is not selective for a -point ultrafilter from CH. We also produce ZFC examples of Fréchet spaces where countable subsets are first countable which are not -selective. All of the notions will be defined in the talk, joint work with Paul Szeptycki.
The talk will be held at the usual time and place on Friday, February 14 in Fields 210 from 1:30 to 3:00. If you will attend the talk, please register using the following link:
Boise Extravaganza in Set Theory, Ashland, OR, June 17-18, 2020
Conference
2/12
We are pleased to announce that the 2020 Boise Extravaganza in Set Theory will take place in Ashland, Oregon, on the campus of Southern Oregon University, during June 17–18.
BEST is an international conference featuring talks on a broad range of recent advances in research in set theory and related fields. Researchers from all areas of logic are welcome. BEST particularly aims to support the careers of young researchers in set theory and logic. The conference is organized by the Set Theory group at Boise State University and is structured as a symposium of the annual meeting of the AAAS, Pacific Division.
Site: https://www.boisestate.edu/math/best/
Contact: best@boisestate.edu
Organizers: Liljana Babinkostova (Boise State University), John Clemens (Boise State University), Samuel Coskey (Boise State University), Marion Scheepers (Boise State University) Scientific support Natasha Dobrinen (University of Denver)
Plenary speakers:
* David Fernández-Bretón (Universidad Nacional Autónoma de México)
* Victoria Gitman (CUNY Graduate Center)
* Jun Le Goh (University of Wisconsin)
* Lynne Yengulalp (University of Dayton and Wake Forest University)
* Joseph Zielinski
* … more to come!
The NSF supports travel grants for student and postdoctoral speakers at BEST. (If you are in another category and could use funding, let us know as well.) We strongly encourage members of groups underrepresented in mathematics to apply! Please visit the conference web site for application instructions.
Tagged: David Fernández-Bretón, Jun Le Goh, Lynne Yengulalp, Joseph Zielinski, Victoria Gitman
Ultrafilters and Ultraproducts Across Mathematics, Pisa, Italy, May 31-June 6, 2020
Conference
2/11/2020
ULTRAMATH 2020
Ultrafilters and Ultraproducts Across Mathematics and Related Topics
May 31 - June 6, 2020, Pisa, Italy
http://people.dm.unipi.it/ultramath2020/
Dear all,
We are happy to announce the upcoming event "ULTRAMATH 2020 - Ultrafilters and Ultraproducts Across Mathematics and Related Topics", that will be held in Pisa (Italy) from May 31st to June 6th 2020.
The international Conference "ULTRAMATH 2020” aims to present recent results in the whole spectrum of mathematics which are grounded on the use of ultrafilters and ultraproducts.
Its main goals:
• Disseminate information about the various techniques related to the use of ultrafilters and ultraproducts, and their potential to attack open problems.
• Bring together researchers with different backgrounds, and encourage their collaborations and interactions, especially on topics connecting different areas of mathematics.
The covered topics of UltraMath 2020 include (but are not limited to):
• Additive and Combinatorial Number Theory.
• Combinatorics and Ramsey Theory.
• Algebra and Geometry.
• General Topology.
• Measure Theory.
• Ergodic Theory and Dynamics.
• Functional Analysis and Metric Spaces.
• Nonstandard Analysis and Model Theory.
• Generalized Spaces and Differential Equations.
• Set Theory.
Greater prominence will be given to those results that satisfy (most of) the following conditions:
• The results can be formulated and presented in non-specialist terms, and be in principle understandable by any practicing mathematician.
• The usage of ultrafilters/ultraproducts is important (or even essential) in obtaining these results.
• The results connect different areas of mathematics.
• The results reveal new facets of known important topics.
This is the second edition of “UltraMath”, after the one held in Pisa in 2008: http://people.dm.unipi.it/ultramath.
Scientific Committee:
Vitaly Bergelson (Ohio State University, USA)
Andreas Blass (University of Michigan, USA)
Mauro Di Nasso (Università di Pisa, Italia)
Renling Jin (College of Charleston, USA)
Organizing Committee:
Mauro Di Nasso (Università di Pisa, Italia) – chair
Lorenzo Luperi Baglini (Università di Milano, Italia)
LIST OF INVITED SPEAKERS
Vieri Benci — Università di Pisa, Italia
Vitaly Bergelson — Ohio State University, USA
Andreas Blass — University of Michigan Ann Arbor, USA
Artem Chernikov — University of California Los Angeles (UCLA), USA
Natasha Dobrinen — University of Denver, USA
Cornelia Druţu — University of Oxford, UK
Victoria Gitman — City University of New York (CUNY), USA
Isaac Goldbring — University of California Irvine (UCI), USA
C. Ward Henson – University of Illinois Urbana-Champaign, USA
Neil Hindman — Howard University, USA
Michael Hrušák — Universidad Nacional Autónoma, México
Renling Jin — College of Charleston, USA
Steven Leth — University of Northern Colorado, USA
Martino Lupini — Victoria University, New Zealand
Joel Moreira — University of Warwick, UK
Jaroslav Nešetřil — Charles University Praha, Czech Republic
Florian Richter – Northwestern University, USA
David A. Ross — University of Hawaii, USA
Sławomir Solecki — Cornell University, USA
Dona Strauss — University of Hull, UK
Simon Thomas — Rutgers University, USA
Stevo Todorcevic — Univ. of Toronto, Canada and Univ. Paris Diderot, France
There will be a call for contributed papers. Moreover, depending on the funds available, participation of young researchers and researchers from disadvantages areas will be supported.
You can preregister by sending an email to ultramath2020@cs.dm.unipi.it with your name and institution.
Updated information about UltraMath 2020 will be posted on the website: http://people.dm.unipi.it/ultramath2020/.
Those who need more information, can contact the organizers at: ultramath2020@cs.dm.unipi.it.
We hope to see you in Pisa!
Best regards,
The Organizers
Tagged: Vieri Benci, Vitaly Bergelson, Andreas Blass, Artem Chernikov, Natasha Dobrinen, Cornelia Druţu, Victoria Gitman, Isaac Goldbring, C. Ward Henson, Neil Hindman, Michael Hrušák, Renling Jin, Steven Leth, Martino Lupini, Joel Moreira, Jaroslav Nešetřil, Florian Richter, David A. Ross, Sławomir Solecki, Dona Strauss, Simon Thomas, Stevo Todorcevic
Logic Colloquium, Poznań, Poladn, July 13-18, 2020
Conference
2/10/2020
Logic Colloquium 2020
Call for Papers
July 13-18, 2020, Poznań, Poland
https://lc2020.pl/
* The Logic Colloquium is the European Summer Meeting of the Association for Symbolic Logic, which in 2020 will be
held from 13th to 18th of July at the Adam Mickiewicz University, Poznań, Poland. It is organized jointly by the
AMU Faculties: of Psychology and Cognitive Science and of Mathematics and Computer Science.
* Registration is now open.
* Important dates:
- March 31st, 2020 deadline for abstract submission
- April 13th, 2020 deadline for student travel awards applications
- April 30th, 2020 notifications
- May 25th, 2020 camera-ready abstracts due
- June 13th, 2020 early payments deadline
- July 7th, 2020 late payments deadline
* Goedel Lecture: Elisabeth Bouscaren (CNRS - Université Paris-Sud)
* Tutorial Speakers: Krzysztof Krupiński (University of Wrocław), Andrew Marks (University of California Los Angeles)
* Plenary Speakers: Linda Westrick (Pennsylvania State University), Benoit Monin (Créteil University), Noam Greenberg
(Victoria University of Wellington), Vera Fischer (University of Viena), Luca Motto Ros (University of Turin),
Elaine Pimentel (Federal University of Rio Grande do Norte), Frank Pfenning (Carnegie Mellon University),
Johan van Benthem (University of Amsterdam), Ryan Williams (Massachusetts Institute of Technology),
Artem Chernikov (University of California Los Angeles)
* Detailed information can be found on the webpage.
Tagged: Elisabeth Bouscaren, Krzysztof Krupiński, Andrew Marks, Linda Westrick, Benoit Monin, Noam Greenberg, Vera Fischer, Luca Motto Ros, Elaine Pimentel, Frank Pfenning, Johan van Benthem, Ryan Williams, Artem Chernikov
This Week in Logic at CUNY
This Week in Logic at CUNY
2/9/2020
This Week in Logic at CUNY:
- - - - Monday, Feb 10, 2020 - - - -
Logic and Metaphysics Workshop Date: Monday, February 10, 4.15-6.15 Place: Room 7395, CUNY Graduate Center Melissa Fusco (Columbia) Is Free Choice Cancellable?
I explore the implications of the Tense Phrase deletion operation known as sluicing (Ross 1969) for the semantic and pragmatic literature on the Free Choice effect (Kamp 1973, von Wright 1969). I argue that the time-honored ‘I don’t know which’-riders on Free Choice sentences, traditionally taken to show that the effect is pragmatic, are sensitive to scope. Careful attention to such riders suggests that these sluices do not show cancellation on Free Choice antecedents in which disjunction scopes narrower than the modal.
- - - - Tuesday, Feb 11, 2020 - - - -
- - - - Wednesday, Feb 12, 2020 - - - -
NO TALKS TODAY - LINCOLN'S BIRTHDAY
Today's New York City Category Theory Seminar talk by Tai-Danae Bradley has been rescheduled for March 11.
- - - - Thursday, Feb 13, 2020 - - - -
- - - - Friday, Feb 14, 2020 - - - -
Logic Workshop CUNY Graduate Center, Room 6417 Friday, February 14, 2:00-3:30pm
Bartosz Wcisło, University of Warsaw Tarski boundary
Our talk concerns axiomatic theories of truth predicates. They are theories obtained by adding to Peano Arithmetic (PAPA) a fresh predicate T(x)T(x) with the intended reading 'xx is (a code of) a true sentence in the language of arithmetic' together with some axioms governing newly added predicate.
The canonical example of such a theory is CT−CT− (Compositional Truth). Its axioms state that the truth predicate is compositional. For instance, a conjunction is true iff both conjuncts are. If we add to CT−CT− full induction in the extended language, we call the resulting theory CTCT.
It is easy to check that CTCT is not conservative over PAPA, i.e., it proves new arithmetical sentences. On the other hand, by a nontrivial theorem of Kotlarski, Krajewski, and Lachlan, CT−CT− extends PAPA conservatively.
In our talk, we will discuss results on the strength of theories between CT−CT− and CTCT. It turns out that the natural axioms concerning purely truth theoretic properties of the newly added predicate (as opposed to axiom schemes which are consequences of induction in more general context) are typically either conservative or exactly equal to CT0CT0, the theory of compositional truth with Δ0Δ0-induction. Thus CT0CT0 turns out to be a surprisingly robust theory and, arguably, the minimal 'natural' non-conservative theory of truth.
Next Week in Logic at CUNY:
- - - - Monday, Feb 17, 2020 - - - -
- - - - Tuesday, Feb 18, 2020 - - - -
- - - - Wednesday, Feb 19, 2020 - - - -
MOPA (Models of Peano Arithmetic) CUNY Graduate Center, Room 4213.03 (Math Thesis Room) Wednesday, February 19, 6:30-8:00pm
James Geiser Soundness and the Gödel Undecidability Theorem
The goal of Gödel’s argument that the theory (T) of Peano Arithmetic is not complete, was to show that the Gödel sentences, GG , and it’s negation, are not provable in T, unless T is inconsistent. In this paper we examine the first half of this argument, namely, that from a hypothetical derivation, PGPG, of GG, a derivation, PfPf, can be constructed that ends in a contradiction. We make the observation that the Gödel argument depends on the metatheory concept of representability that, in turn, depends on the metatheory concept of soundness. Our analysis leads to two main observations, the first well know, and the second, a challenge to the standard undecidability argument.
1 – The existence of PGPG implies that T is unsound. This conclusion does not require the further construction, from PGPG, of the derivation PfPf.
2 - We argue that effectuation of the construction of PfPf is obstructed, because that effectuation requires acceptance of a contradiction in the metatheory regarding the soundness of T.
This is joint work with Catherine Hennix.
The New York City Category Theory Seminar Department of Computer Science, Department of Mathematics The Graduate Center of The City University of New York Date and Time: Wednesday February 19, 2020, 7:00 - 8:30 PM., Room 6417. Speaker: Todd Trimble, Western Connecticut State University. Title: The Universal Property of the Bar Construction.
Abstract: The bar construction is a fundamental construction used throughout homological algebra and algebraic topology, including for example the construction of classifying bundles, deloopings of suitable H-spaces, and free resolutions of general algebras and the cohomology thereof. The underlying theme is that the bar construction produces canonical contractible or acyclic simplicial algebras, as usually explained by the acyclic models theorem. In this talk we sharpen this result, giving a precise sense in which the bar construction is a universal acyclic simplicial algebra, here recasting "acyclic" not as a property but as an algebraic structure, whereby acyclic structures are coalgebras over the decalage comonad.
- - - - Thursday, Feb 20, 2020 - - - -
- - - - Friday, Feb 21, 2020 - - - -
Logic Workshop CUNY Graduate Center, Room 6417 Friday, February 21, 2:00-3:30pm Andrey Morozov, Novosibirsk State University On ΣΣ-preorderings in HF(R) We prove that ω1ω1 cannot be embedded into any preordering ΣΣ-definable with parameters in the hereditarily finite superstructure over the ordered field of real numbers, HF(R). As corollaries, we obtain characterizations of ΣΣ-presentable ordinals and Gödel constructive sets of kind LαLα. It also follows that there are no ΣΣ-presentations for structures of TT-, mm-, 11-, and tttt-degrees over HF(R).
- - - - Other Logic News - - - -
CONFERENCE ANNOUNCEMENT:
The “Sao Paulo School of Advanced Science on Contemporary Logic, Rationality and Information - SPLogIC”, sponsored by FAPESP and promoted by the Centre for Logic, Epistemology and the History of Science (CLE) of the University of Campinas (Unicamp), Brazil, will be held at Unicamp from July 13th to 24th, 2020.
The School celebrates the 90th anniversary of Newton da Costa and aims at: providing an overview of the state-of-art methodology and research on contemporary logic (featuring non-classical logics), rationality, and information.
The program comprises 9 courses and 9 plenary talks delivered in English by experts in each topic, as well as oral presentations (LED Talks) and poster sessions by the students.
Topics to be covered include:
• History and Philosophy of Paraconsistent Logics
• The Australian, Belgian, Brazilian, and Israeli schools on paraconsistency
• Logic and Reasoning, Logic and Information, Logic and Argumentation
• Methodological aspects on interpreting, translating and combining logics
• Logic, Probability and Artificial Intelligence.
The event will select 100 fully-funded participants (50 grantees from all states of Brazil and 50 international grantees). Funding includes airfare, medical insurance, accommodation and meals throughout the two weeks.
Undergraduate students, graduate students and postdoctoral fellows (up to 5 years after completion of the Ph.D) from all countries are encouraged to apply.
Applications are open from January 15th to February 22th, 2020.
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
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Wednesday seminar
Prague Set Theory Seminar
2/7/2020
Dear all,
The seminar meets on Wednesday February 12th at 11:00 in the Institute
of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: The program is not yet determined, presumably either Jonathan
Verner or I will talking about something.
Best,
David
Udine Workshop on Singular Cardinals, Udine, Italy, July 6-7, 2020
Conference
2/7/2020
Udine Workshop on Singular Cardinals
We are happy to announce the upcoming "Udine Workshop on Singular Cardinals", that will be held in Udine (Italy) on 6-7 July 2020. It will be held at Palazzo di Toppo Wassermann, a prestigious 18th-century palace. Singular cardinals are transversal to set theory and beyond, and this will be an occasion to bring together researchers working on singular cardinals and share the latest developments on this topic.
Organizers:
Vincenzo Dimonte (University of Udine)
Mirna Dzamonja (The University of East Anglia)
Luca Motto Ros (University of Torino)
Talks:
James Cummings (Carnegie Mellon University)
Péter Komjáth (Eötvös Loránd University)
Menachem Magidor (The Hebrew University of Jerusalem) *
Itay Neeman (UCLA) *
Assaf Rinot (Bar-Ilan University)
Jouko Väänänen (University of Helsinki)
* To confirm
Website: https://users.dimi.uniud.it/~vincenzo.dimonte/WSC2020.html
There will be some slots open for contributed talks, and all the interested researchers and students are encouraged to apply. To propose a contributed talk, please write to vincenzo.dimonte@uniud.it by May the 31st.
For further information, contact vincenzo.dimonte@uniud.it
Tagged: James Cummings, Péter Komjáth, Menachem Magidor, Itay Neeman, Assaf Rinot, Jouko Väänänen
(KGRC) research seminar talk on WEDNESDAY, February 12
Kurt Godel Research Center
2/6/2020
The KGRC welcomes as guests:
Jana Marikova (host: Benjamin Miller) will stay until June 30.
Clifton Ealy (host: Benjamin Miller) will visit from March 7 to March 15 and
from May 9 to June 30.
Miguel Moreno (host: Lyubomyr Zdomskyy) will stay until November 30.
Vincenzo Dimonte (host: Sy-David Friedman) will stay from February 8 to
February 13 and give a talk on February 12 (see below).
Martin Zeman (hosts: Sandra Müller and Monroe Eskew) will visit end of February
or early March (to be determined) and give a talk on March 5 (tentative date).
Jerzy Kakol (host: Damian Sobota) will stay from March 29 to April 4 and give a
talk on April 2.
Chi Tat Chong (host: Sy-David Friedman) will stay from June 17 to June 19 and
give a talk on June 18.
* * *
Research seminar
Kurt Gödel Research Center
WEDNESDAY, February 12
(Please note the unusual day.)
"Regularity properties in singular generalized descriptive set theory"
Vincenzo Dimonte (University of Udine, Italy)
Generalized descriptive set theory is the study of definable subsets of the
space ${}^\kappa 2$ with the bounded topology. Such study has been
overwhelmingly focussed on the case with $\kappa$ regular. Motivated by the
theory of rank-into-rank cardinals, we concentrated instead on the case of
$\kappa$ singular of cofinality $\omega$, painting a picture that is quite
similar to the classical descriptive set theory case. This talk is going to
center around the generalization of regularity properties (Perfect Set Property
and Baire Property) in this context. The PSP is still akin to the classical
case, while the BP probably needs more large-cardinal power to be non-trivial.
Time and Place
Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47)
Talk at 4:00pm in the KGRC lecture room (seminar room D5.48)
Universität Wien
Institut für Mathematik
Kurt Gödel Research Center
Augasse 2-6, UZA 1 - Building 2
1090 Wien
This Week in Logic at CUNY
This Week in Logic at CUNY
2/3/2020
Hi everyone,
This is the first edition of "This Week in Logic" in this new semester and new decade - welcome back! Future mailings will occur weekly on Sunday evenings.
Best,
Jonas Reitz
This Week in Logic at CUNY:
- - - - Tuesday, Feb 4, 2020 - - - -
- - - - Wednesday, Feb 05, 2020 - - - -
MOPA (Models of Peano Arithmetic) CUNY Graduate Center, Room 4213.03 (Math Thesis Room) Wednesday, Feb 5, 6:30-8:00pm Athar Abdul-Quader, Purchase College The pentagon saga continues
I will continue to speak about Jim Schmerl's recent paper on the pentagon lattice N5N5. In this talk, I will outline the main result that no model of PA has a 'mixed' elementary extension such that the resulting interstructure lattice is isomorphic to the pentagon.
- - - - Thursday, Feb 06, 2020 - - - -
- - - - Friday, Feb 07, 2020 - - - -
Logic Workshop CUNY Graduate Center, Room 6417 Friday, Feb 7, 2:00-3:30pm Victor Selivanov, Institute of Informatics Systems, Novosibirsk A Q-Wadge hierarchy in quasi-Polish spaces
The Wadge hierarchy was originally defined and studied only in the Baire space (and some other zero-dimensional spaces). We extend it to arbitrary topological spaces by providing a set-theoretic definition of all its levels. We show that our extension behaves well in second countable spaces and especially in quasi-Polish spaces. In particular, all levels are preserved by continuous open surjections between second countable spaces, which implies, e.g., several Hausdorff-Kuratowski-type theorems in quasi-Polish spaces. In fact, many results hold not only for the Wadge hierarchy of sets but also for its extension to Borel functions from a space to a countable better quasiorder Q.
Next Week in Logic at CUNY:
- - - - Monday, Feb 10, 2020 - - - -
Logic and Metaphysics Workshop Date: Monday, February 10, 4.15-6.15 Place: Room 7395, CUNY Graduate Center Melissa Fusco (Columbia). Title: A Deontic Logic for Two Paradoxes of Deontic Modality
Abstract: In this paper, we take steps towards axiomatizing the two dimensional deontic logic in Fusco (2015), which validates a form of free choice permission (von Wright 1969, Kamp 1973; (1) below) and witnesses the nonentailment known as Ross’s Puzzle (Ross 1941; (2) below).
(1) You may have an apple or a pear ⇒ You may have an apple, and you may have a pear. (2) You ought to post the letter = ̸⇒ You ought to post the letter or burn it.
Since <>(p or q) = (<>p ∨ <>q) and [ ](p) ⇒ [ ](p ∨ q) are valid in any normal modal logic – including standard deontic logic – the negations of (1)-(2) are entrenched in modal proof systems. To reverse them without explosion will entail excavating the foundations of the propositional tautologies. The resulting system pursues the intuition that classical tautologies involving disjunctions are truths of meaning, rather than propositional necessities. This marks a departure from the commitments the propositional fragment of a modal proof system is standardly taken to embody.
Note: This is joint work with Arc Kocurek (Cornell).
- - - - Tuesday, Feb 11, 2020 - - - -
- - - - Wednesday, Feb 12, 2020 - - - -
The New York City Category Theory Seminar Department of Computer Science, Department of Mathematics The Graduate Center of The City University of New York Speaker: Tai-Danae Bradley, The Graduate Center, CUNY. Date and Time: Wednesday February 12, 2020, 7:00 - 8:30 PM., Room 6417. Title: TBA. Abstract: TBA.
- - - - Thursday, Feb 13, 2020 - - - -
- - - - Friday, Feb 14, 2020 - - - -
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
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If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Set theory seminar this week: Assaf Shani
Toronto Set Theory Seminar
2/3/2020
Hi everyone,
This week Assaf Shani from Carnegie Mellon University will speak in the seminar. His talk is entitled "Borel reducibility and symmetric models."
Abstract: We develop a correspondence between Borel equivalence relations induced by closed subgroups of and symmetric models of set theory without choice, and apply it to prove a conjecture of Hjorth-Kechris-Louveau (1998). For example, we show that the equivalence relation is strictly below in Borel reducibility. By results of Hjorth-Kechris-Louveau, bounds the complexity of actions of , while bounds the complexity of actions of "well behaved'' closed subgroups of , such as abelian groups. The notions mentioned above will be defined in the talk, and I will also survey the results of Hjorth-Kechris-Louveau.
The talk will be held on Friday, February 7 in Fields 210 from 1:30 to 3:00. If you will attend the talk, please register using the following link:
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 12 February 2020, 17:00 hrs
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Ashutosh Kumar
Title: On some problems in set-theoretic Eucildean Ramsey theory
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: We shall discuss some questions in Euclidean Ramsey theory where
techniques from set theory have played a role.
Wednesday seminar
Prague Set Theory Seminar
1/30/2020
Dear all,
The seminar meets on Wednesday February 5th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
We will have quests speakers from Morelia. The main program is:
César Corral -- Frechet-like properties in almost disjoint families
Abstract: We will study some strong Frechet properties and properties
very related to the preservation of Frechetness under products. Our main
tool to construct counterexamples to some implications between them will
be the use of almost disjoint families.
Time permitting, there might be more topics/speakers.
Best,
David
Tagged: César Corral
Logic Seminar
Barcelona Logic Seminar
1/29/2020 10:09:59
Next session of the Logic Seminar
Asaf Karagila
Newton International Fellow, School of Mathematics, UEA (Norwich)
THE POWER OF POWER SETS OF COUNTABLE UNIONS OF COUNTABLE SETS
Wednesday, February 5.
12:30
IMUB Lecture Room, Facultat de Matemàtiques i Informàtica, UB.
Aquest missatge, i els fitxers adjunts que hi pugui haver, pot contenir informació confidencial o protegida legalment i s’adreça exclusivament a la persona o entitat destinatària. Si no consteu com a destinatari final
o no teniu l’encàrrec de rebre’l, no esteu autoritzat a llegir-lo, retenir-lo, modificar-lo, distribuir-lo, copiar-lo ni a revelar-ne el contingut. Si l’heu rebut per error, informeu-ne el remitent i elimineu del sistema tant el missatge com els fitxers adjunts
que hi pugui haver.
Este mensaje, y los ficheros adjuntos que pueda incluir, puede contener información confidencial o legalmente protegida y está exclusivamente dirigido a la persona o entidad destinataria. Si usted no consta como destinatario final ni es la persona encargada
de recibirlo, no está autorizado a leerlo, retenerlo, modificarlo, distribuirlo o copiarlo, ni a revelar su contenido. Si lo ha recibido por error, informe de ello al remitente y elimine del sistema tanto el mensaje como los ficheros adjuntos que pueda contener.
This email message and any attachments it carries may contain confidential or legally protected material and are intended solely for the individual or organization to whom they are addressed. If you are not the intended recipient of this message or the person
responsible for processing it, then you are not authorized to read, save, modify, send, copy or disclose any part of it. If you have received the message by mistake, please inform the sender of this and eliminate the message and any attachments it carries
from your account.
Re: Set Theory Seminar
Barcelona Set Theory Seminar
1/24/2020
Dear Colleagues,
Please find attached the announcement of the next session of the Barcelona Set Theory seminar.
Eduardo Sealtiel Martínez Mendoza: Teoría PCF e hipótesis del continuo generalizada revisada
Mexico City Logic Seminar
1/24/2020
Con la teoría de las posibles cofinalidades de Shelah tenemos una herramienta que nos permite estudiar a más profundidad la operación de exponenciación cardinal. Uno de los resultados más destacados que podemos obtener a partir de esta teoría es que si 2^{\aleph_0}<\aleph_{\omega_4}, entonces \aleph_{\omega}^{\aleph_0}<\aleph_{\omega_4}. Otro resultado igual de interesante está relacionado con uno de los problemas centrales de teoría de conjuntos.
Sabemos que la hipótesis del continuo generalizada es equivalente a que para cualesquiera cardinales regulares \lambda>\kappa, \lambda^\kappa=\lambda.. Este enunciado se puede aproximar a partir del nivel de cualquier cardinal límite fuerte si consideramos una modificación de la operación de exponenciación cardinal. A esta aproximación se le llama hipótesis del continuo generalizada revisada de Shelah, la cual tiene como consecuencias algunos resultados de carácter combinatorio. Por ejemplo, a partir del primer cardinal límite fuerte, la hipótesis del continuo generalizada es equivalente al principio diamante de Jensen. También, podemos acotar a la celularidad de algunas álgebras booleana con cardinales específicos.
Tagged: Eduardo Sealtiel Martínez Mendoza
Logic Seminar Wed 29 Jan 2020 17:00 hrs at NUS - Talk by Wang Wei
NUS Logic Seminar
1/22/2020
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 29 January 2019, 17:00 hrs
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Wang Wei, Sun Yat-Sen University, Guangzhou
Title: Non-standard models of arithmetic and their standard systems.
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
PA is the first order fragment of Peano's axiomatization of the natural
numbers. The natural numbers, N, is called the standard model of PA. But by
compactness theorem in first order logic, there are also models of PA
different from N, which are called non-standard models of arithmetic. Like
in N, every element of a non-standard model M has a binary expansion, which
can be regarded as the characteristic function of a subset of N. The
standard system of M is the collection of all such subsets of N. It is
known that standard systems of non-standard models are always Scott sets
and every Scott set of cardinality less than or equal to the first
uncountable cardinal is the standard system of some non-standard model.
However, the general Scott set problem, whether every Scott set is the
standard system of some non-standard model, remains one of the major open
problems in the model theory of arithmetic. This talk will present some
history of Scott set problem, as well as two constructions of non-standard
models with uncountable standard systems.
Tagged: Wang Wei
Set Theory Seminar in the Stewart Library this week
Toronto Set Theory Seminar
1/22/2020
Hi everyone,
After some negotiation, we were upgraded to the Stewart Library on the third floor for this week. Here is the info:
Speaker: Henry Yuen
Title: Connes' Embedding Problem through the lens of complexity theory
Location: Fields Institute Stewart Library (#309)
Date and time: Friday, January 24 2020, 1:30-3:00.
Thanks,
Bill
Wednesday seminar
Prague Set Theory Seminar
1/22/2020
Dear all,
There is no seminar next week, Wednesday January 29th, there are however
still spots to participate the Winter School next week.
https://www.winterschool.eu/
The seminars in February are to be decided.
No announcement = no seminar.
Best,
David
(KGRC) research seminar talk on Thursday, January 30
Kurt Godel Research Center
1/22/2020
The KGRC welcomes as guests:
Jana Marikova (host: Benjamin Miller) will stay until June 30.
Clifton Ealy (host: Benjamin Miller) will visit from March 7 to March 15
and from May 9 to June 30.
Miguel Moreno (host: Lyubomyr Zdomskyy) will stay until November 30 and
give a talk on January 23.
Leandro Aurichi (host: Lyubomyr Zdomskyy) will stay until January 31.
Jerzy Kakol (host: Damian Sobota) will stay from March 29 to April 4 and
give a talk on April 2.
Chi Tat Chong (host: Sy-David Friedman) will stay from June 17 to June 19
and give a talk on June 18.
* * *
Research seminar
Kurt Gödel Research Center Thursday, January 30
"Construction with opposition: Cardinal invariants and games"
Víctor Torres-Pérez (TU Wien)
We consider several game versions of the cardinal invariants $\mathfrak t$,
$\mathfrak u$ and $\mathfrak a$. We show that the standard proof that
parametrized diamond principles prove that the cardinal invariants are small
actually shows that their game counterparts are small. On the other hand we
show that $\mathfrak t < \mathfrak t_{Builder}$ and $\mathfrak u < \mathfrak
u_{Builder}$ are both relatively consistent with ZFC, where $\mathfrak
t_{Builder}$ and $\mathfrak u_{Builder}$ are the principal game versions of
$\mathfrak t$ and $\mathfrak u$, respectively. The corresponding question for
$\mathfrak a$ remains open.
This is a joint work with Jörg Brendle and Michael Hru\v{s}'ak.
Time and Place
Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47)
Talk at 4:00pm in the KGRC lecture room (seminar room D5.48)
Universität Wien
Institut für Mathematik
Kurt Gödel Research Center
Augasse 2-6, UZA 1 - Building 2
1090 Wien
The talk will be held on Friday, January 24 in the Fields Institute from 1:30 to 3:00.
I expect that the seminar will be of broad interest, so please invite your colleagues working in relevant areas to attend. If you will attend the talk, please register using the following link http://www.surveygizmo.com/s3/3247294/Seminar-Registration and send me a reply email indicating your interest, so that I can secure a larger room than our usual meeting place (Fields 210) if needed.
See you there,
Bill Chen
Tagged: Henry Yuen
Set theory seminar tomorrow: Spencer Unger
Toronto Set Theory Seminar
1/16/2020
Hi everyone,
This week Spencer Unger will speak in the seminar. IMPORTANT: note the change in time and place!
The talk will be held on Friday, January 17 in Huron 1018 from 10:00 to 11:00. If you will attend the talk, please register using the following link:
Location: the Huron Building is located on Huron Street adjacent to the Fields Institute and the Bahen Centre. Our room is a seminar room located on the 10th floor. To access this room, please take the elevator to the 9th floor and then walk up one flight of stairs. I will leave from the Fields Institute to the seminar location shortly before the seminar begins.
See you there,
Bill Chen
Tagged: Spencer Unger
Wednesday seminar
Prague Set Theory Seminar
1/14/2020
Dear all,
There is no seminar tomorrow Wednesday January 15th.
The seminar meets again next week, Wednesday January 22nd at 11:00 in
the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor,
front building.
Program: Egbert Thümmel will speak about omega_1 injective ideals in
Boolean algebras, and Jan Šaroch will talk about applications of
injective ideals (and set theory in general) in abstract algebra (modules).
Best,
David
Tagged: Egbert Thümmel
(KGRC) PhD defense and other upcoming talks
Kurt Godel Research Center
1/14/2020
The KGRC welcomes as guests:
Jana Marikova (host: Benjamin Miller) will stay until June 30, 2020.
Clifton Ealy (host: Benjamin Miller) will stay until January 11, then
visit again March 7 to March 15 and May 9 to June 30.
Miguel Moreno (host: Lyubomyr Zdomskyy) will stay until November 30, 2020
and give a talk on January 23 (see below).
Corey Switzer (host: Vera Fischer) will stay from January 12 to January 19
and give a talk on January 16 (see below).
Leandro Aurichi (host: Lyubomyr Zdomskyy) will stay from January 15 to
January 31.
Jerzy Kąkol (host: Damian Sobota) will stay from March 29 to April 4 and give a
talk on April 2.
Chi Tat Chong (host: Sy-David Friedman) will give a talk on June 18, 2020.
* * *
PhD Defense
Kurt Gödel Research Center
Wednesday, January 15
"Generalized notions of recurrence: Bases and the
existence of invariant probability measures"
Jürgen Manuel Inselmann (KGRC)
We establish basis and anti-basis theorems for a broad collection of recurrence
notions appearing in descriptive, measurable, and topological dynamics, and
show that such notions cannot characterize the existence of invariant
probability measures in the deacriptive milieu.
Time and Place
Talk at 10:00am in the KGRC lecture room (seminar room D5.48)
Universität Wien
Institut für Mathematik
Kurt Gödel Research Center
Augasse 2-6, UZA 1 - Building 2
1090 Wien
* * *
Research seminar
Kurt Gödel Research Center
Thursday, January 16
"Generalized Cardinal Characteristics for Sets of Functions"
Corey Bacal Switzer (City University of New York, Graduate Center, USA)
Cardinal characteristics on the generalized Baire and Cantor spaces
$\kappa^\kappa$ and $2^\kappa$ have recently generated significant interest. In
this talk I will introduce a different generalization of cardinal
characteristics, namely to the space of functions $f:\omega^\omega \to
\omega^\omega$. Given an ideal $\mathcal I$ on Baire space and a relation $R$
let us define $f R_{\mathcal I} g$ for $f$ and $g$ functions from
$\omega^\omega$ to $\omega^\omega$ if and only if $f(x) R g(x)$ for an
$\mathcal I$-measure one set of $x \in \omega^\omega$. By letting $\mathcal I$
vary over the null ideal, the meager ideal and the bounded ideal; and $R$ vary
over the relations $\leq^*$, $\neq^*$ and $\in^*$ we get 18 new cardinal
characteristics by considering the bounding and dominating numbers for these
relations. These new cardinals form a diagram of provable implications similar
to the Cichoń diagram. They also interact in several surprising ways with the
cardinal characteristics on $\omega$. For instance, they can be arbitrarily
large in models of CH, yet they can be $\aleph_1$ in models where the continuum
is arbitrarily large. They are bigger in the Sacks model than the Cohen model.
I will introduce these cardinals, show some of the provable implications and
discuss what is known about consistent inequalities, including new
generalizations of well-known forcing notions on the reals to this context.
This includes joint work with Jörg Brendle.
Time and Place
Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47)
Talk at 4:00pm in the KGRC lecture room (seminar room D5.48)
Universität Wien
Institut für Mathematik
Kurt Gödel Research Center
Augasse 2-6, UZA 1 - Building 2
1090 Wien
* * *
Research seminar
Kurt Gödel Research Center
Thursday, January 23
"Fake Reflection"
Miguel Moreno (Bar-Ilan University, Ramat Gan, Tel Aviv, Israel)
Motivated from many results in generalized descriptive set theory, Filter
Reflection (aka Fake Reflection) is an abstract version of reflection
compatible with large cardinals, forcing axioms, but also V=L.
In this talk we will present the motivation and definition of filter
reflection, we will explain how to force filter reflection and how to
force its failure. We will also show some applications and properties of
filter reflection, e.g. the consistency of "$E_{\omega_1}^\kappa$ filter
reflects to a subset of $E_{\omega}^\kappa$".
Time and Place
Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47)
Talk at 4:00pm in the KGRC lecture room (seminar room D5.48)
Universität Wien
Institut für Mathematik
Kurt Gödel Research Center
Augasse 2-6, UZA 1 - Building 2
1090 Wien
Colloquium this week: Spencer Unger
Toronto Set Theory Seminar
1/13/2020
Hi everyone,
There will be a special colloquium this week given by Spencer Unger of the Hebrew University entitled "A constructive solution to Tarski's circle squaring problem."
The talk will be held in Bahen Centre 6183 on Wednesday, January 15 at 4:00 pm.
Invitation to the Logic Seminar at the National University of Singapore
(1) Date: Wednesday, 15 January 2020, 17:00 hrs
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Frank Stephan
Title: Measure and Conquer for Max Hamming Distance XSAT
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
This talk gives an overview of the joint work of the speaker's
recent work on the Hamming XSAT problem. This problem asks for an
algorithm to determine which, given an XSAT instance, determines
the maximum Hamming distance between two solutions of this instance.
The problem has been studied by Dahloef in 2005 in an ISAAC paper
who provided an O(1.83848^n) algorithm for this problem.
Later Fu, Zhu and Yin presented at JFCST 2012 an O(1.6760^n)
algorithm for the related Max Hamming X3SAT problem where all clauses
have at most three literals. The current paper provides for the
general Max Hamming XSAT problem an O(1.4983^n) algorithm
which applies also the technique "Measure and Conquer"
in order to prove a better bound than the algorithm would give
otherwise. Furthermore, the algorithm does not only provide the
maximum Hamming distance of two solutions of the instance, but
instead for each k between 0 and n the number
of pairs of solutions which have Hamming distance k.
For the special case Max Hamming Distant X3SAT, Hoi, Jain and Stephan
have the bound O(1.3298^n) at the conference FSTTCS 2019.
(2) Date: Wednesday, 22 January 2020, 17:00 hrs
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Asger Dag Toernquist, Kobenhavns Universitet
Title: Mad, med, mcg and other maximal combinatorial objects.
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
This talk is about the descriptive set theory and infinitary combinatorics.
In the past 6 years, a number of long-standing problems related to the
definability (in the sense of effective descriptive set theory) of
so-called maximal almost disjoint (mad) families, maximal eventually
different (med) families, and maximal cofinitary groups (mcg) have been
solved by an array of authors. I will give an overview of these developments.
Almost disjoint families are families of infinite subsets of omega
where any two distinct elements of the family intersect finitely;
eventually different families are families of functions from omega to omega
such that any two distinct functions in the family are eventually different;
and cofinitary groups are subgroups of the group of all permutations of omega
with the property that all non-identity elements of the group have at most
finitely many fixed points. Maximality of such objects in all cases means
maximal under inclusion (among such families).
A classical result due to Adrian Mathias states that no analytic infinite
mad families. A slew of recent results shed light on this classical
result by showing that under suitable descriptive set-theoretic
regularity assumptions, there are no mad families at all (and this
localizes to suitable pointclasses, especially to analytic sets).
In a totally unexpected twist, Horowitz and Shelah showed in 2016
that there are Borel med families and mcg, solving a long-standing
problem. I will finish the talk by discussing some related, still
unsolved problems, especially the following: Is there a maximal
(infinite) analytic set of pairwise Turing-incomparable reals?
Wednesday seminar
Prague Set Theory Seminar
1/3/2020
Dear all,
The seminar meets on Wednesday January 8th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
The program is not yet determined, walk-in speakers will be welcome.
Best,
David
(KGRC) research seminar talk Thursday, January 9
Kurt Godel Research Center
12/30/2019
The KGRC welcomes as guests:
Jana Marikova (host: Benjamin Miller) will stay until June 30, 2020.
Clifton Ealy (host: Benjamin Miller) will stay until January 11, then
visit again March 7 to March 15 and May 9 to June 30.
Miguel Moreno (host: Lyubomyr Zdomskyy) will stay until November 30, 2020
and give a talk on January 23.
Taras Banakh (host: Lyubomyr Zdomskyy) will stay until January 3.
Jaroslav Šupina (host: Vera Fischer) will stay from January 8 to January
10 and give a talk on January 9 (see below).
Corey Switzer (host: Vera Fischer) will stay from January 12 to January 19
and give a talk on January 16.
Leandro Aurichi (host: Lyubomyr Zdomskyy) will stay from January 15 to
January 31.
Chi Tat Chong (host: Sy-David Friedman) will give a talk on June 18, 2020.
* * *
Research seminar
Kurt Gödel Research Center
Thursday, January 9
"Ideal pseudointersection numbers and topological spaces"
Jaroslav Šupina
(Pavol Jozef Šafárik University in Košice, Slovakia)
Investigations of ideal versions of selection principles pointed our
attention to pseudointersection numbers introduced by P.
Borodulin-Nadzieja and B. Farkas 2012 and M. Repický 2018. Both
modifications of pseudointersection number are parametrized by ideals on
natural numbers and related to orderings among such ideals.
We shall focus on these invariants and their connections to selection
principles. Their topological characterizations (which resemble
Fréchet-Urysohn property) are simple tool to derive inequalities among
them. Finally, a result by P. Borodulin-Nadzieja and B. Farkas 2012 shows
that ideal version of standard characterization of countable
Fréchet-Urysohn property via selection principle by J. Gerlits and Zs.
Nagy 1982 is not true.
Time and Place
Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47)
Talk at 4:00pm in the KGRC lecture room (seminar room D5.48)
Universität Wien
Institut für Mathematik
Kurt Gödel Research Center
Augasse 2-6, UZA 1 - Building 2
1090 Wien
Maciej Malicki, Continuous Logic VI
IMPAN Working Group in Applications of Set Theory
12/15/2019
Seminar: Working group in applications of set theory, IMPAN
Thursday, 19.12.2019,
Group lunch (optional): meeting at the reception of IMPAN at 12.30, going elsewhere, "Wiesz co Zjesz" will be closed
Seminar at 2:15 pm, room 105, IMPAN, Śniadecki 8, Warsaw.
Speaker: Maciej Malicki (Warsaw School of Economics, SGH)
Title: "Continuous logic VI"
Abstact: "This series of talks will be devoted to a gentle introduction to continuous logic - a natural generalization of first-order logic that is suitable in studying mathematical objects equipped with a metric, e.g. Polish metric spaces and groups, Banach spaces, C*-algebras, etc. Continuous logic is surprisingly parallel to classical logic, and all fundamental concepts such as definable sets, algebraic sets, type spaces, quantifier elimination, omitting types, imaginaries, stability, etc., have their counterparts in this setting.
In the final talk, I will define the notion of principal type, and prove the Ryll-Nardzewski theorem for continuous logic.
Literature: Ben Yaacov, Itai; Berenstein, Alexander; Henson, C. Ward; Usvyatsov, Alexander; Model theory for metric structures. Model theory with applications to algebra and analysis. Vol. 2, 315--427, London Math. Soc. Lecture Note Ser., 350, Cambridge Univ. Press, Cambridge, 2008.".
Visit our seminar webpage which may include announcements of some future talks at https://www.impan.pl/~set_theory/Seminar/
Cheers, Piotr.
(KGRC) research seminar talk Thursday, December 19
Kurt Godel Research Center
12/12/2019
The KGRC welcomes as guests:
Jana Marikova (host: Benjamin Miller) will stay until June 30, 2020.
Clifton Ealy (host: Benjamin Miller) will stay until January 11, then
visit again March 7 to March 15 and May 9 to June 30.
Miguel Moreno (host: Lyubomyr Zdomskyy) will stay until November 30, 2020 and
give a talk on January 23.
Oleksandr Ravsky (host: Lyubomyr Zdomskyy) will stay until December 22.
Taras Banakh (host: Lyubomyr Zdomskyy) will stay from December 17 to
January 3 and give a talk on December 19 (see below).
Jaroslav Supina (host: Vera Fischer) will stay from January 8 to January 10 and
give a talk on January 9.
Corey Switzer (host: Vera Fischer) will stay from January 12 to January 19
and give a talk on January 16.
Leandro Aurichi (host: Lyubomyr Zdomskyy) will stay from January 15 to January
31.
Chi Tat Chong (host: Sy-David Friedman) will give a talk on June 18, 2020.
* * *
Research seminar
Kurt Gödel Research Center
Thursday, December 19
"The Golomb space is topologically rigid"
Taras Banakh
(Ivan Franko National University of Lviv, Ukraine)
The Golomb space is the space $\mathcal N$ of natural numbers endowed with the
topology generated by the base consisting of arithmetic progressions
$a+b\mathbb N$ with coprime parameters $a$ and $b$. The Golomb space is one of
the simplest examples of a countable connected Hausdorff space.
In this space Topology and Arithmetic are tightly intertwined. We survey
topological properties of the Golomb space and prove that this space is
topologically rigid, i.e., has trivial homeomorphism group. This resolves a
problem posed on Mathoverflow in 2017. Philosophically, the topological
rigidity of the Golomb space can be interpreted as the possibility to encode in
Topology all Arithmetics (which encodes all Mathematics by the Godel
arithmetization).
Time and Place
Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47)
Talk at 4:00pm in the KGRC lecture room (seminar room D5.48)
Universität Wien
Institut für Mathematik
Kurt Gödel Research Center
Augasse 2-6, UZA 1 - Building 2
1090 Wien
Wednesday seminar
Prague Set Theory Seminar
12/11/2019
Dear all,
The seminar meets on Wednesday December 18th at 11:00 in the Institute
of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Jan Grebík -- Hyperfinite equivalence relations
Jan will discuss some questions and results concerning hyperfiniteness
of Borel equivalence relations both in Borel and measure setting.
Let me also remind you that the pre-Christmas meeting of the employees
and friends of the Institute of Mathematics CAS does take place on
Wednesday after the seminar, at 16:00 in the Institute.
Best,
David
Set theory seminar this week: Dilip Raghavan
Toronto Set Theory Seminar
12/10/2019
Hi everyone,
This week Dilip Raghavan from the National University of Singapore will speak about Galvin's problem in higher dimensions.
The talk will be held on Friday, December 13 in Fields 210 from 1:30 to 3:00. If you will attend the talk, please register using the following link:
Please make note to change the date to December 13 for registration.
See you there,
Bill Chen
Ultrafilters and Ultraproducts Across Mathematics, Pisa, Italy, May 31-June 6, 2020
Conference
12/10/2019
ULTRAMATH 2020
Ultrafilters and Ultraproducts Across Mathematics and Related Topics
May 31 - June 6, 2020, Pisa, Italy
http://people.dm.unipi.it/ultramath2020/
Dear all,
We are happy to announce the upcoming event "ULTRAMATH 2020 - Ultrafilters and Ultraproducts Across Mathematics and Related Topics", that will be held in Pisa (Italy) from May 31st to June 6th 2020.
The international Conference "ULTRAMATH 2020” aims to present recent results in the whole spectrum of mathematics which are grounded on the use of ultrafilters and ultraproducts.
Its main goals:
• Disseminate information about the various techniques related to the use of ultrafilters and ultraproducts, and their potential to attack open problems.
• Bring together researchers with different backgrounds, and encourage their collaborations and interactions, especially on topics connecting different areas of mathematics.
The covered topics of UltraMath 2020 include (but are not limited to):
• Additive and Combinatorial Number Theory.
• Combinatorics and Ramsey Theory.
• Algebra and Geometry.
• General Topology.
• Measure Theory.
• Ergodic Theory and Dynamics.
• Functional Analysis and Metric Spaces.
• Nonstandard Analysis and Model Theory.
• Generalized Spaces and Differential Equations.
• Set Theory.
Greater prominence will be given to those results that satisfy (most of) the following conditions:
• The results can be formulated and presented in non-specialist terms, and be in principle understandable by any practicing mathematician.
• The usage of ultrafilters/ultraproducts is important (or even essential) in obtaining these results.
• The results connect different areas of mathematics.
• The results reveal new facets of known important topics.
This is the second edition of “UltraMath”, after the one held in Pisa in 2008: http://people.dm.unipi.it/ultramath.
Scientific Committee:
Vitaly Bergelson (Ohio State University, USA)
Andreas Blass (University of Michigan, USA)
Mauro Di Nasso (Università di Pisa, Italia)
Renling Jin (College of Charleston, USA)
Organizing Committee:
Mauro Di Nasso (Università di Pisa, Italia) – chair
Lorenzo Luperi Baglini (Università di Milano, Italia)
LIST OF INVITED SPEAKERS
Vieri Benci — Università di Pisa, Italia
Vitaly Bergelson — Ohio State University, USA
Andreas Blass — University of Michigan Ann Arbor, USA
Artem Chernikov — University of California Los Angeles (UCLA), USA
Natasha Dobrinen — University of Denver, USA
Cornelia Druţu — University of Oxford, UK
Victoria Gitman — City University of New York (CUNY), USA
Isaac Goldbring — University of California Irvine (UCI), USA
C. Ward Henson – University of Illinois Urbana-Champaign, USA
Neil Hindman — Howard University, USA
Michael Hrušák — Universidad Nacional Autónoma, México
Renling Jin — College of Charleston, USA
Steven Leth — University of Northern Colorado, USA
Martino Lupini — Victoria University, New Zealand
Joel Moreira — University of Warwick, UK
Jaroslav Nešetřil — Charles University Praha, Czech Republic
Florian Richter – Northwestern University, USA
David A. Ross — University of Hawaii, USA
Sławomir Solecki — Cornell University, USA
Dona Strauss — University of Hull, UK
Simon Thomas — Rutgers University, USA
Stevo Todorcevic — Univ. of Toronto, Canada and Univ. Paris Diderot, France
There will be a call for contributed papers. Moreover, depending on the funds available, participation of young researchers and researchers from disadvantages areas will be supported.
You can preregister by sending an email to ultramath2020@cs.dm.unipi.it with your name and institution.
Updated information about UltraMath 2020 will be posted on the website: http://people.dm.unipi.it/ultramath2020/.
Those who need more information, can contact the organizers at: ultramath2020@cs.dm.unipi.it.
We hope to see you in Pisa!
Best regards,
The Organizers
Tagged: Vieri Benci, Vitaly Bergelson, Andreas Blass, Artem Chernikov, Natasha Dobrinen, Cornelia Druţu, Victoria Gitman, Isaac Goldbring, C. Ward Henson, Neil Hindman, Michael Hrušák, Renling Jin, Steven Leth, Martino Lupini, Joel Moreira, Jaroslav Nešetřil, Florian Richter, David A. Ross, Sławomir Solecki, Dona Strauss, Simon Thomas, Stevo Todorcevic
Logic and Theory Seminar: December 10, 3:00 - 3:50 pm
Boise Logic and Set Theory Seminar
12/9/2019
Colleagues,
The speaker for the final meeting of the Fall 2019 Logic and Set Theory seminar is Dr. Samuel Coskey of the Department of Mathematics. Details are as follows:
Location: Mathematics Building Room 124
Date/time: Tuesday, December 10, 3:00 - 3:50 pm
Title: Locally finite groups and automorphisms
Abstract: The class of finite groups is an amalgamation class, which means that they admit a “Fraisse limit” - a countable structure which contains all the finite groups and which is highly self-symmetric. The limit group is called Hall’s group, it is locally finite, and has the property that any isomorphic finite subgroups are conjugate. In this talk we will give background on Hall’s group and discuss constructing automorphisms of Hall’s group.
Regards,
Marion
Distinguished Professor
Department of Mathematics
Boise State University
Boise, ID 83725
U.S.A.
Tagged: Samuel Coskey
This Week in Logic at CUNY
This Week in Logic at CUNY
12/8/2019
This Week in Logic at CUNY:
Hi everyone,
This will be the last regular edition "This Week in Logic at CUNY" until after the winter break (end of January 2020). Special announcements will be sent as necessary in the meantime.
Happy Holidays to all,
Jonas
- - - - Monday, Dec 9, 2019 - - - -
Logic and Metaphysics Workshop Date: Monday, December 9, 4.15-6.15 Place: Room 7314, CUNY Graduate Center
Mark Colyvan (Sydney) Title: Logic in Fiction
Abstract: This paper will address the question of whether the logic of a fiction can be specified as part of the fiction. For example, can one tell a fictional story in which it is part of the story that the logic in question is, say, K3? It seems unproblematic that we can do this. After all, we can tell a story about a world with a different geometry from ours, different physical laws, and even different numbers of dimensions (e.g. the two-dimensional world of Flatland). While allowing fictions to specify their own logics seems a natural extension of such science fiction, there are problems looming. Fictions are, by their very nature, incomplete. Specifying that the logic in question is classical is to embrace, amongst other things, classical principles such as excluded middle. But if the fictional world is incomplete, in what sense can it be part of the story that excluded middle holds? We would, in effect, be specifying that the incomplete situation described in the fiction is complete. Imposing excluded middle where it doesn’t belong leads to contradiction. These are especially pressing issues for (particular kinds of) fictionalism about mathematics.
- - - - Tuesday, Dec 10, 2019 - - - -
Computational Logic Seminar Time 2:00 - 4:00 PM, Room 5382, Tuesday, December 10 Speaker: Sergei Artemov, CUNY Graduate Center Title: Proving schemes in Peano arithmetic.
Abstract: We will sketch a theory of proving schemes {F(n) | n=0,1,2,…} in Peano arithmetic PA. Obviously, the naïve approach “prove each F(n) in PA” does not work since its justification can easily spill beyond PA. We offer a well-principled definition of a proof of a scheme and establish its basic properties: decidability of proofs, computable enumerability of provable schemes, conservativety of proving schemes (no new theorems), etc. Overall: proving schemes is an intriguing research avenue.
We will then discuss how this theory has influenced our recent proof of PA-consistency. A spoiler: only an explanatory influence, putting the formalized proof of consistency into its rightful place among proofs of schemes in PA.
- - - - Wednesday, Dec 11, 2019 - - - -
- - - - Thursday, Dec 12, 2019 - - - -
- - - - Friday, Dec 13, 2019 - - - -
Friday, December 13, 4:15 PM Seminar in Logic, Games and Language CUNY Graduate Center (365 Fifth Avenue, Room 4421) Glenn Shafer (Rutgers) Using Game Theory to Reunify Subjective and Objective Probability.
Abstract. Belief and frequency co-existed in the calculus of games of chance as it was taught in Europe beginning in the 13th century. They still co-existed in the theory of mathematical probability that Jacob Bernoulli based on that calculus. But they came apart in the middle of the 19th century. In this talk, I show how game theory can bring them back together. My new book with Volodya Vovk (Game-Theoretic Foundations for Probability and Finance, Wiley, May 2019) bases mathematical probability on a game with three players: Forecaster (who offers bets), Skeptic (who decides which offers to take), and Reality (who decides the outcomes). Forecaster is the Bayesian. Skeptic is the frequentist. See the working papers at www.probabilityandfinance.com.
Next Week in Logic at CUNY:
- - - - Monday, Dec 16, 2019 - - - -
- - - - Tuesday, Dec 17, 2019 - - - -
- - - - Wednesday, Dec 18, 2019 - - - -
- - - - Thursday, Dec 19, 2019 - - - -
- - - - Friday, Dec 20, 2019 - - - -
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Wednesday seminar
Prague Set Theory Seminar
12/6/2019
Dear all,
The seminar meets on Wednesday December 11th at 11:00 in the Institute
of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Martin Doležal -- A Turán-type theorem for large-distance
graphs in Euclidean spaces
Turán’s theorem, a classical result in graph theory, provides an upper
bound on the number of edges in any graph with n vertices and with no
complete subgraphs on k vertices. We are interested in analogous results
for so called large-distance graphs. A large-distance graph is a
measurable graph whose vertex set is a measurable subset of Euclidean
space, and two vertices are connected by an edge if and only if their
distance is larger that 2. We ask for upper bounds on the measures of
vertices and edges of a large-distance graph with no complete subgraphs
on k vertices. One of our main results says that if A is a measurable
subset of a plane such that the large-distance graph of A does not
contain any complete subgraph on three vertices then the 2-dimensional
Lebesgue measure of A is at most 2π.
This is a joint work with J. Hladký, J. Kolář, T. Mitsis, C. Pelekis and
V. Vlasák.
Best,
David
Tagged: Martin Doležal
This Week in Logic at CUNY
This Week in Logic at CUNY
12/1/2019
This Week in Logic at CUNY:
- - - - Monday, Dec 2, 2019 - - - -
Logic and Metaphysics Workshop Date: Monday, December 2, 4.15-6.15 Place: Room 7314, CUNY Graduate Center
Jessica Wilson (Toronto) Title: On the Notion of Diachronic Emergence
Abstract: Though most accounts of emergence take this to be a broadly synchronic phenomenon, it has been recently maintained that there are distinctively diachronic forms of emergence (see, e.g., O’Connor and Wong’s 2005 account of strong emergence, Mitchell’s 2012 dynamic self-organization account of emergence, and Humphreys’ and Sartenaer and Guay’s 2016 accounts of ‘transformational emergence’). Here I argue that there is no need for a distinctively diachronic notion of emergence, as purported cases of such emergence can either be subsumed under broadly synchronic accounts, or else are better seen as simply cases of causation.
- - - - Tuesday, Dec 3, 2019 - - - -
Computational Logic Seminar Time 2:00 - 4:00 PM, Room 5382, Tuesday, December 3 Speaker: Sergei Artemov, CUNY Graduate Center Title: The Provability of Consistency: Interactive Discussion II.
Abstract: We offer a proof of PA-consistency by means of PA. In a nutshell, we view the consistency definition as scheme “S is not a proof of a contradiction in PA” and i) prove this scheme “given an arbitrary finite sequence of formulas S”; ii) formalize (i) in PA to secure that no tools outside PA have been used.
We continue with technical details of the proof and its place in the proof theory of PA. As a related thread, we outline the theory of proving arithmetical schemes in PA in a general setting. Our proof is a) contentual consistency proof followed by b) comprehensive formalization of (a) in PA. We discuss why the “standard” approach to proving consistency i) formalization of consistency (either as a formula or a scheme); ii) proving the resulted formalized consistency in PA, is plain wrong at both conceptual and technical levels.
We will then conclude with the promised series of aggregated Q&A's from the previous talks, lectures and discussions.
- - - - Wednesday, Dec 4, 2019 - - - -
The New York City Category Theory Seminar Department of Computer Science, Department of Mathematics The Graduate Center of The City University of New York
Speaker: Philipp Rothmaler, The Graduate Center and BCC. Date and Time: Wednesday December 4, 2019, 7:00 - 8:30 PM., Room 6417. Title: Martsinkovsky-Russell torsion done definably.
Abstract: I will show that the torsion radical in question is, in every module, a (usually infinite) sum of first-order definable subgroups (of the additive group) of the module. Moreover, the collection of formulas involved is uniform: it is all the so-called pp (=positive primitive) formulas that vanish in flat modules. Among the consequences are many of the known features of that torsion theory, as well as new ones. Besides, this lays the foundation for other pp definable torsion radicals, which I will discuss time permitting. Note, the formulas in question constitute functors, namely subfunctors of the forgetful functor.
- - - - Thursday, Dec 5, 2019 - - - -
Computer Science Colloquium December 5, 2019 (Thursday), 4:15 PM, CUNY Graduate Center, Room TBA Yde Venema, ILLC, Universiteit van Amsterdam Bisimulation invariance: an approach via tree automata
In process theory, at the interface of logic and theoretical computer science, one represents a computational process as a transition system, that is: a collection of states that satisfy certain properties, and are linked by transition relations. For the specification and verification of desired behavior one uses formal logical languages to describe these systems. Since a process can have many distinct representations, one is interested in languages that are expressive enough to express the relevant properties of the process, but not the irrelevant details of its representation. An important notion of equivalence on transition systems is that of a bisimulation: states that are bisimilar (linked by a bisimulation) can be considered to be indistinguishable. As a consequence, properties of states that are not invariant under bisimulations are irrelevant. In this context, it is of interest to identify the bisimulation-invariant fragment of some yardstick logic: If a logic M corresponds to the bisimulation-invariant fragment of a yardstick logic L, then M is strong enough to express all relevant properties of L.
- - - - Friday, Dec 6, 2019 - - - -
Model Theory Seminar CUNY Graduate Center, Room 6417 Friday, December 6, 12:30-2:00pm Rizos Sklinos, Stevens Institute of Technology Fields definable in the theory of nonabelian free groups
In this talk I will show that only finite fields are definable in the theory of nonabelian free groups. This is joint work with Ayala Byron.
Logic Workshop CUNY Graduate Center, Room 6417 Friday, December 6, 2:00-3:30pm Chris Laskowski, University of Maryland Counting siblings Two countable structures are siblings if each is embeddable into the other (e.g., any two countable non-scattered linear orders are siblings). Clearly if M and N are siblings, they have the same finite substructures, hence have the same universal theories. We characterize the universal theories in a finite, relational language that have a countable model with 2ℵ02ℵ0 siblings. This is joint work with Sam Braunfeld.
Next Week in Logic at CUNY:
- - - - Monday, Dec 9, 2019 - - - -
Logic and Metaphysics Workshop Date: Monday, December 9, 4.15-6.15 Place: Room 7314, CUNY Graduate Center
Mark Colyvan (Sydney) Title: Logic in Fiction
Abstract: This paper will address the question of whether the logic of a fiction can be specified as part of the fiction. For example, can one tell a fictional story in which it is part of the story that the logic in question is, say, K3? It seems unproblematic that we can do this. After all, we can tell a story about a world with a different geometry from ours, different physical laws, and even different numbers of dimensions (e.g. the two-dimensional world of Flatland). While allowing fictions to specify their own logics seems a natural extension of such science fiction, there are problems looming. Fictions are, by their very nature, incomplete. Specifying that the logic in question is classical is to embrace, amongst other things, classical principles such as excluded middle. But if the fictional world is incomplete, in what sense can it be part of the story that excluded middle holds? We would, in effect, be specifying that the incomplete situation described in the fiction is complete. Imposing excluded middle where it doesn’t belong leads to contradiction. These are especially pressing issues for (particular kinds of) fictionalism about mathematics.
- - - - Tuesday, Dec 10, 2019 - - - -
- - - - Wednesday, Dec 11, 2019 - - - -
- - - - Thursday, Dec 12, 2019 - - - -
- - - - Friday, Dec 13, 2019 - - - -
READING DAY
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Maciej Malicki, Continuous Logic V
IMPAN Working Group in Applications of Set Theory
12/1/2019
Seminar: Working group in applications of set theory, IMPAN
Thursday, 5.12.2019,
Group lunch (optional): meeting at the reception of IMPAN at 12.30, going to www.wieszcozjesz.pl/1-Danie-dnia (the menu will update)
Seminar at 2:15 pm, room 105, IMPAN, Śniadecki 8, Warsaw.
Speaker: Maciej Malicki (Warsaw School of Economics, SGH)
Title: "Continuous logic V"
Abstact: "This series of talks will be devoted to a gentle introduction to continuous logic - a natural generalization of first-order logic that is suitable in studying mathematical objects equipped with a metric, e.g. Polish metric spaces and groups, Banach spaces, C*-algebras, etc. Continuous logic is surprisingly parallel to classical logic, and all fundamental concepts such as definable sets, algebraic sets, type spaces, quantifier elimination, omitting types, imaginaries, stability, etc., have their counterparts in this setting.
In the fifth talk, I will finish discussing spaces of types, and take a look at the concept of definability in metric structures.
Literature: Ben Yaacov, Itai; Berenstein, Alexander; Henson, C. Ward; Usvyatsov, Alexander; Model theory for metric structures. Model theory with applications to algebra and analysis. Vol. 2, 315--427, London Math. Soc. Lecture Note Ser., 350, Cambridge Univ. Press, Cambridge, 2008.".
Visit our seminar webpage which may include announcements of some future talks at https://www.impan.pl/~set_theory/Seminar/
Cheers, Piotr.
Tagged: Maciej Malicki
Logic Seminar 2 Dec 2019 17:00 hrs NUS S17#04-05 by R Hoelzl (correction of room)
NUS Logic Seminar
11/27/2019
Invitation to the Logic Seminar at the National University of Singapore
Date: Monday, 02 December 2019, 17:00 hrs
Room: S17#04-05, Department of Mathematics, NUS
Speaker: Rupert Hoelzl, University of the Bundeswehr, Munich
Title: Randomness for computable measures and complexity
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
We study the possible growth rates of the Kolmogorov complexity of
initial segments of sequences that are random with respect to some
computable measure on the Cantor Space, the so-called proper sequences.
Our main results are as follows:
(1) We show that the initial segment complexity of a proper sequence X
is bounded from below by a computable function (that is, X is complex)
if and only if X is random with respect to some computable, continuous
measure.
(2) We prove that a uniform version of the previous result fails to hold:
there is a family of complex sequences that are random with respect to
a single computable measure such that for every computable, continuous
measure mu, some sequence in this family fails to be random with
respect to mu.
(3) We show that there are proper sequences with extremely
slow-growing initial segment complexity, that is, there is a proper
sequence the initial segment complexity of which is infinitely often
below every computable function, and even a proper sequence the
initial segment complexity of which is dominated by all computable
functions.
(4) We prove various facts about the Turing degrees of such
sequences and show that they are useful in the study of certain
classes of pathological measures on the Cantor Space, namely
diminutive measures and trivial measures.
This is joint work with Christopher P. Porter and a paper is
available at https://arxiv.org/abs/1510.07202; it also appeared
in the Annals of Pure and Applied Logic, 168(4):860-886, 2017.
See https://doi.org/10.1016/j.apal.2016.10.014 for more
information.
Tagged: Rupert Hoelzl
Wednesday seminar
Prague Set Theory Seminar
11/27/2019
Dear all,
The seminar meets on Wednesday December 4th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Stevo Todorcevic -- A survey of Tukey theory
Old and recent results about the Tukey classification scheme will be
presented.
Problems and research directions will also be presented.
Best,
David
PS: Let me also remind you that the Cech lecture delivered by Stevo
Todorcevic will take place next week on Tuesday at 10:30 in the
Institute, and that the Colloquiumfest meeting
http://users.math.cas.cz/kubis/2019/22colloquiumfest/ starts next Friday.
Tagged: Stevo Todorcevic
Philipp Lücke: Definable pathological sets
Bonn Logic and Set Theory Seminar
11/27/2019
Philipp Lücke
University of Bonn
Definable pathological sets
Logic and Set Theory Seminar
27th November 2019, 3:00 pm – 4:30 pm
Fry Building, G.07
Set-theoretic objects whose construction requires the Axiom of Choice are often referred to as pathological sets. For many types of pathological sets of real numbers, results from descriptive set theory can be used to show that these objects cannot be defined by simple formulas in second-order arithmetic. In this talk, I want to present results dealing with the set theoretic definability of pathological objects of higher cardinalities, focussing on long well-orderings and maximal almost disjoint families of subsets of uncountable cardinals. I will present results dealing with the following aspects of this topic: (i) the existence of such objects at ω1 in determinacy models, (ii) the Σ1-definability of these sets at ω1 in the presence of large cardinals, and (iii) the Σ1-definability of such objects above a measurable cardinal. This is joint work in progress with Sandra Müller (Vienna).
Tagged: Philipp Lücke
Logic Seminar 2 Dec 2019 17:00 hrs at NUS by R Hoelzl
NUS Logic Seminar
11/26/2019
Invitation to the Logic Seminar at the National University of Singapore
Date: Monday, 02 December 2019, 17:00 hrs
Room: S17#06-11, Department of Mathematics, NUS
Speaker: Rupert Hoelzl, University of the Bundeswehr, Munich
Title: Randomness for computable measures and complexity
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
We study the possible growth rates of the Kolmogorov complexity of
initial segments of sequences that are random with respect to some
computable measure on the Cantor Space, the so-called proper sequences.
Our main results are as follows:
(1) We show that the initial segment complexity of a proper sequence X
is bounded from below by a computable function (that is, X is complex)
if and only if X is random with respect to some computable, continuous
measure.
(2) We prove that a uniform version of the previous result fails to hold:
there is a family of complex sequences that are random with respect to
a single computable measure such that for every computable, continuous
measure mu, some sequence in this family fails to be random with
respect to mu.
(3) We show that there are proper sequences with extremely
slow-growing initial segment complexity, that is, there is a proper
sequence the initial segment complexity of which is infinitely often
below every computable function, and even a proper sequence the
initial segment complexity of which is dominated by all computable
functions.
(4) We prove various facts about the Turing degrees of such
sequences and show that they are useful in the study of certain
classes of pathological measures on the Cantor Space, namely
diminutive measures and trivial measures.
This is joint work with Christopher P. Porter and a paper is
available at https://arxiv.org/abs/1510.07202; it also appeared
in the Annals of Pure and Applied Logic, 168(4):860-886, 2017.
See https://doi.org/10.1016/j.apal.2016.10.014 for more
information.
Tagged: Rupert Hoelzl
(KGRC) upcoming talks in the research seminar
Kurt Godel Research Center
11/25/2019
The KGRC welcomes as guests:
Jana Marikova (host: Benjamin Miller) will stay until June 30, 2020.
Clifton Ealy (host: Benjamin Miller) will stay until January 11, then
visit again March 7 to March 15 and May 9 to June 30.
Istvan Juhasz (host: Sy-David Friedman) will stay from November 25 to
December 1 and give a talk on November 28 (see below).
Miguel Moreno (host: Lyubomyr Zdomskyy) will stay from December 1, 2019 to
November 30, 2020 and give a talk on January 23.
Mohammad Golshani (hosts: Sy-David Friedman, Yair Hayut) will stay from
December 4 to December 11 and give a talk on December 5 (see below).
Oleksandr Ravsky (host: Lyubomyr Zdomskyy) will stay from December 9 to
December 22 and give a talk on December 12.
Taras Banakh (host: Lyubomyr Zdomskyy) will stay from December 17 to
January 3 and give a talk on December 19.
Jaroslav Supina (host: Vera Fischer) will stay from January 8 to January
10 and give a talk on January 9.
Corey Switzer (host: Vera Fischer) will stay from January 12 to January 19
and give a talk on January 16.
Chi Tat Chong (host: Sy-David Friedman) will give a talk on June 18, 2020.
* * *
Research seminar
Kurt Gödel Research Center
Thursday, November 28
"Large cardinals in topology"
Istvan Juhasz
(Renyi Mathematical Institute, Budapest, Hungary)
In this talk I intend to deal with a number of problems of general
topology that, sometimes rather naturally but sometimes quite
surprisingly, lead to or boil down to statements of set theory involving
various large cardinals.
Time and Place
Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47)
Talk at 4:00pm in the KGRC lecture room (seminar room D5.48)
Universität Wien
Institut für Mathematik
Kurt Gödel Research Center
Augasse 2-6, UZA 1 - Building 2
1090 Wien
* * *
Research seminar
Kurt Gödel Research Center
Thursday, December 5
"Specializing trees"
Mohammad Golshani
(Institute for Research in Fundamental Sciences (IPM), Tehran, Iran)
We review our recent work on specializing trees on higher cardinals. The
results are based on several joint works with Aspero, Hayut and Shelah.
Time and Place
Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47)
Talk at 4:00pm in the KGRC lecture room (seminar room D5.48)
Universität Wien
Institut für Mathematik
Kurt Gödel Research Center
Augasse 2-6, UZA 1 - Building 2
1090 Wien
Set theory seminar this week: Chris Lambie-Hanson
Toronto Set Theory Seminar
11/25/2019
Hello,
This week, Chris Lambie-Hanson from Virginia Commonwealth University will speak in the seminar. The title of his talk is "Set theoretic compactness and higher derived limits."
Abstract: Issues of set theoretic compactness frequently arise when considering questions about derived functors. In particular, the non-vanishing of such derived functors is often witnessed by a concrete combinatorial instance of set theoretic incompactness.
In this talk, we will discuss some recent results about the derived functors of the inverse limit functor. We will focus on a specific inverse system of abelian groups, , that arose in Mardešić and Prasolov's work on the additivity of strong homology and has since arisen independently in a number of contexts. Our main result states that, relative to the consistency of a weakly compact cardinal, it is consistent that the -th derived limits vanish simultaneously for all . We will sketch a proof of this fact and then discuss the extent to which certain generalizations of this result can hold. This is joint work with Jeffrey Bergfalk.
The talk will be held on Friday, November 29 in Fields 210 from 1:30 to 3:30. If you will attend the talk, please register using the following link:
Please make note to change the date to the date of the seminar (November 29) for registration.
Have a good week,
Bill Chen
This Week in Logic at CUNY
This Week in Logic at CUNY
11/24/2019
This Week in Logic at CUNY:
- - - - Monday, Nov 25, 2019 - - - -
Logic and Metaphysics Workshop Date: Monday, November 11, 4.15-6.15 Place: Room 7314, CUNY Graduate Center
Vincent Alexis Peluce (CUNY) Title: Memory and Intuitionistic Logic
Abstract: L.E.J. Brouwer writes, “people try by means of sounds and symbols to originate in other people copies of the mathematical constructions and reasonings which they have made themselves; by the same means they try to aid their own memory. In this way the mathematical language comes into being, and as its special case the language of logical reasoning” (1907). More is left to be said, however, about the relation between the Brouwerian subject and logical language. In this talk we discuss the usual account of this relation and some problems with that view. We then propose an alternative.
- - - - Tuesday, Nov 26, 2019 - - - -
Computational Logic Seminar Time 2:00 - 4:00 PM, Room 5382, Tuesday, November 26 Speaker: Sergei Artemov, CUNY Graduate Center Title: The Provability of Consistency: Interactive Discussion.
Abstract: Both Hilbert and Gödel objected to viewing Gödel’s Second Incompleteness Theorem as yielding impossibility of proving consistency of a theory by means of the same theory and thus as blocking Hilbert’s consistency program; it was von Neumann who promoted such a reading. Widely popularized, von Neumann’s interpretation is based on two assumptions: 1. Gödel’s consistency formula is the only way to formalize consistency. 2. Any contentual reasoning using principles from T internalizes as a formal derivation in T. We show that already for Peano arithmetic PA, both of these assumptions are false: (1) does not cover such legitimate mode of presentation as schemes (think of the Induction scheme), (2) fails for schemes. This observation renders von Neumann’s claim unwarranted and supports Hilbert’s and Gödel’s skepticism.
Furthermore, we offer a proof of PA-consistency by means of PA. In a nutshell, we view the consistency definition as scheme “S is not a proof of a contradiction in PA” and i) prove this scheme “given an arbitrary finite sequence of formulas S”; ii) formalize (i) in PA to secure that no tools outside PA have been used.
This work has already been widely discussed and we will review the aggregated (long) list of questions and misunderstandings. A teaser: we do not try to derive Gödel’s consistency formula Con(PA) in PA. Moreover, no formal proof in PA can establish mathematical consistency of PA; a successful consistency proof should be contentual.
- - - - Wednesday, Nov 27, 2019 - - - -
The New York City Category Theory Seminar Department of Computer Science, Department of Mathematics The Graduate Center of The City University of New York
Speaker: James Myer Date and Time: Wednesday November 27, 2019, 7:00 - 8:30 PM., Room 6417.
Title: Higher-Order Categorical Logic: TBA.
Abstract: We will be starting at 0.6 and go forward.
- - - - Thursday, Nov 28, 2019 - - - -
THANKSGIVING BREAK
- - - - Friday, Nov 29, 2019 - - - -
THANKSGIVING BREAK
Next Week in Logic at CUNY:
- - - - Monday, Dec 2, 2019 - - - -
Logic and Metaphysics Workshop Date: Monday, December 2, 4.15-6.15 Place: Room 7314, CUNY Graduate Center
Jessica Wilson (Toronto) Title: On the Notion of Diachronic Emergence
Abstract: Though most accounts of emergence take this to be a broadly synchronic phenomenon, it has been recently maintained that there are distinctively diachronic forms of emergence (see, e.g., O’Connor and Wong’s 2005 account of strong emergence, Mitchell’s 2012 dynamic self-organization account of emergence, and Humphreys’ and Sartenaer and Guay’s 2016 accounts of ‘transformational emergence’). Here I argue that there is no need for a distinctively diachronic notion of emergence, as purported cases of such emergence can either be subsumed under broadly synchronic accounts, or else are better seen as simply cases of causation.
- - - - Tuesday, Dec 3, 2019 - - - -
- - - - Wednesday, Dec 4, 2019 - - - -
The New York City Category Theory Seminar Department of Computer Science, Department of Mathematics The Graduate Center of The City University of New York
Speaker: Philipp Rothmaler, The Graduate Center and BCC. Date and Time: Wednesday December 4, 2019, 7:00 - 8:30 PM., Room 6417. Title: Martsinkovsky-Russell torsion done definably.
Abstract: I will show that the torsion radical in question is, in every module, a (usually infinite) sum of first-order definable subgroups (of the additive group) of the module. Moreover, the collection of formulas involved is uniform: it is all the so-called pp (=positive primitive) formulas that vanish in flat modules. Among the consequences are many of the known features of that torsion theory, as well as new ones. Besides, this lays the foundation for other pp definable torsion radicals, which I will discuss time permitting. Note, the formulas in question constitute functors, namely subfunctors of the forgetful functor.
- - - - Thursday, Dec 5, 2019 - - - -
Computer Science Colloquium December 5, 2019 (Thursday), 4:15 PM, CUNY Graduate Center, Room TBA Yde Venema, ILLC, Universiteit van Amsterdam Bisimulation invariance: an approach via tree automata
In process theory, at the interface of logic and theoretical computer science, one represents a computational process as a transition system, that is: a collection of states that satisfy certain properties, and are linked by transition relations. For the specification and verification of desired behavior one uses formal logical languages to describe these systems. Since a process can have many distinct representations, one is interested in languages that are expressive enough to express the relevant properties of the process, but not the irrelevant details of its representation. An important notion of equivalence on transition systems is that of a bisimulation: states that are bisimilar (linked by a bisimulation) can be considered to be indistinguishable. As a consequence, properties of states that are not invariant under bisimulations are irrelevant. In this context, it is of interest to identify the bisimulation-invariant fragment of some yardstick logic: If a logic M corresponds to the bisimulation-invariant fragment of a yardstick logic L, then M is strong enough to express all relevant properties of L.
In the talk we introduce the notions of transition systems and bisimulation, and we discuss the bisimulation invariance question for some well-known logics such as first-order and monadic second-order logic. We will mention some recent results that use the notion of alternating tree automata.
This talk is based on joint work with Facundo Carreiro, Alessandro Facchini and Fabio Zanasi.
- - - - Friday, Dec 6, 2019 - - - -
Logic Workshop CUNY Graduate Center, Room 6417 Friday, December 6, 2:00-3:30pm Chris Laskowski, University of Maryland TBA
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
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Wednesday seminar
Prague Set Theory Seminar
11/20/2019
Dear all,
A couple of announcements first:
1)
During December 6--9 (Fri--Mon) the Institute of Mathematics will host
the 22nd Colloquiumfest.
http://users.math.cas.cz/kubis/2019/22colloquiumfest/
Everybody is welcome to attend, there is no conference fee. In order to
register, it is enough to send an email to Beata Kubis
or Wieslaw Kubis with the
relevant data.
2)
On Tuesday December 3rd Stevo Todorcevic will deliver the Cech lecture
in the Institute.
Moreover, Stevo agreed to give a talk at our seminar on Wednesday
December 4th.
The seminar next week meets on Wednesday November 27th at 11:00 in the
Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front
building.
Program: Jovana Obradović agreed to give us a gentle introduction into
her neck of the woods.
Title: Combinatorial homotopy theory for operads
Abstract: It is a classical result of homotopy theory that algebraic
structures with homotopy associative multiplication, such as based loop
spaces, admit a nice combinatorial characterization in terms of
Stasheff's associahedra. Taking operads as the starting algebraic
structure, in this talk we introduce an explicit combinatorial
characterization of their strongly homotopy version. In our description,
the spaces of operations are defined in terms of hypergraph polytopes,
and the composition structure generalizes the one of the Stasheff's
associahedra operad.
Best,
David
UPDATE: This Week in Logic at CUNY
This Week in Logic at CUNY
11/19/2019
Hi everyone,
It's come to my attention that today's talk in the Computational Logic Seminar was erroneously placed under Wednesday, Nov 20 in this week's email. This was human error on my part - the talk was today, Tuesday, Nov 19 (corrected below). My apologies to the speaker and organizers!
Regretfully,
Jonas Reitz
This Week in Logic at CUNY:
- - - - Monday, Nov 18, 2019 - - - -
Logic and Metaphysics Workshop Date: Monday, November 11, 4.15-6.15 Place: Room 7314, CUNY Graduate Center Matías Bulnes (CUNY)
Title: An Unorthodox Solution to the Hintikka-Kripke Problem
Abstract: The Hintikka-Kripke problem consists in reconciling Hintikka’s semantics for doxastic operators and Kripke’s semantics for alethic operators. The problem arises from their treatment of identity. While the necessity of identities was one of the main innovations of Kripke’s semantics, Hintikka needs identities to be contingent to explain the opacity of doxastic operators. Yet alethic and doxastic operators are combined effortlessly in everyday discourse. In the talk, I will first discuss various attempts at reconciliation within the orthodoxy about opacity, and raise objections to them. Then, I will propose an unorthodox idea: rather than thinking of doxastic operators as introducing new possible worlds with different identities, think of them as introducing new logical spaces with different domains of objects. This achieves reconciliation by circumscribing the necessity of identities to the logical space of each agent. To assess this idea viz-a-viz its competitors, we will have to reexamine some fundamental concepts of the problem of opacity, such as the concepts of language and semantics.
- - - - Tuesday, Nov 19, 2019 - - - -
Computational Logic Seminar Time 2:00 - 4:00 PM, Room 5382 Tuesday, November 19 Speaker: Sergei Artemov, CUNY Graduate Center Title: On Logical Foundations of Strategic Games II
Abstract: In his dissertation of 1950, Nash based his concept of the solution to a game on the assumption that “a rational prediction should be unique, that the players should be able to deduce and make use of it”. We study when such definitive solutions exist for strategic games with ordinal payoffs. We show that games without Nash equilibria do not have definitive solutions under any notion of rationality, but each Nash equilibrium can be a definitive solution for an appropriate refinement of Aumann rationality. With respect to Aumann rationality itself, games with multiple Nash equilibria cannot have definitive solutions. Some games with a unique Nash equilibrium have definitive solutions, others don’t, and the criterion for a definitive solution is provided by the iterated deletion of strictly dominated strategies.
- - - - Wednesday, Nov 20, 2019 - - - -
The New York City Category Theory Seminar
Department of Computer Science, Department of Mathematics The Graduate Center of The City University of New York
Speaker: Raymond Puzio. Date and Time: Wednesday November 20, 2019, 7:00 - 8:30 PM., Room 6417. Title: Posets, Lifting properties, and Completions.
Abstract: Ever since Dedekind, it has been known that special classes of posets can be characterized in terms of forbidden configurations. We note how these characterizations result from lifting properties which, in turn, correspond to propositions in regular logic. This leads us to consider subcategories of morphisms between posets and idempotent completions.
- - - - Thursday, Nov 21, 2019 - - - -
- - - - Friday, Nov 22, 2019 - - - -
Set Theory Seminar CUNY Graduate Center, Room 6417 Friday, November 22, 10:00-11:45am
Brent Cody, Virginia Commonwealth University A refinement of the Ramsey hierarchy via indescribability
A subset XX of a cardinal κκ is Ramsey if for every function f:[X]<ωo2f:[X]<ωo2 there is a set H⊆XH⊆X of cardinality κκ which is homogeneous for ff, meaning that f↾[H]nf↾[H]n is constant for each n<ωn<ω. Baumgartner proved that if κκ is Ramsey, then the collection of non-Ramsey subsets of κκ is a normal ideal on κκ. We will discuss some recent results concerning Ramsey properties in which homogeneous sets are demanded to be indescribable of a particular degree. Moreover, by iterating Feng's Ramsey operator, which he used to define a notion of αα-Ramseyness of a cardinal κκ, we will consider hypotheses in which homogeneous sets themselves satisfy various Ramsey properties. For ordinals α,β<κα,β<κ we will define a notion of αα-Π1βΠβ1-Ramseyness of a cardinal κκ where αα indicates how many times the Ramsey operator has been iterated and ββ indicates the degree of transfinite indescribability (due to Sharpe-Welch and independently Bagaria) one initially demands homogeneous to satisfy. We will prove that for α,β<κα,β<κ an αα-Π1βΠβ1-Ramsey cardinal is strictly between Feng's αα-Ramsey and an (α+1α+1)-Ramsey cardinal in consistency strength. Moreover, for fixed α<κα<κ, as ββ increases the αα-Π1βΠβ1-Ramsey cardinals yield a strictly increasing hierarchy, in a somewhat subtle sense. For β0<β1<κβ0<β1<κ and for large enough α<κα<κ, κκ being αα-Π1β0Πβ01-Ramsey is equivalent to κκ being αα-Π1β1Πβ11-Ramsey (we will identify the least αα at which this equivalence occurs). But if α,β0<κα,β0<κ there is a large enough β1<κβ1<κ such that κκ being αα-Π1β0Πβ01-Ramsey is strictly weaker than κκ being αα-Π1β1Πβ11-Ramsey. All of these results seem to require a careful analysis of the ideals associated to the various large cardinal notions.
Model Theory Seminar
CUNY Graduate Center, Room 6417
Friday, November 22, 12:30-2:00pm
Alex Kruckman, Wesleyan University A diversity of Kim's Lemmas
One of the most important steps in the development of simplicity theory by Kim and Pillay in the 1990s was a result now known as Kim's Lemma: In a simple theory, if a formula divides, then this dividing is witnessed by every Morley sequence in the appropriate type. More recently, variants on Kim's Lemma have been shown (by Chernikov, Kaplan, and Ramsey) to follow from, and in fact characterize, the combinatorial dividing lines NTP2 and NSOP1: two generalizations of simplicity in different directions. After surveying the Kim's Lemmas of the past, I will speculate about a new combinatorial dividing line, generalizing both NTP2 and NSOP1 and characterized by a new variant of Kim's Lemma. This is joint speculation with Nick Ramsey.
Logic Workshop CUNY Graduate Center, Room 6417 Friday, November 22, 2:00-3:30pm
Alex Kruckman, Wesleyan University Interpolative fusions
Fix languages L and L' (possibly non-disjoint). An structure M in the union of these languages is interpolative if whenever X is an L-definable set in M and X' is an L'-definable set in M, X and X' intersect unless they are separated by disjoint definable sets in the intersection of L and L'. When T is an L theory and T' is an L' theory, we say that a theory T* is the interpolative fusion of T and T' if it axiomatizes the class of interpolative models of the union of T and T'. If T and T' are model-complete, this is exactly the model companion of the union theory. Interpolative fusions provide a unified framework for studying many examples of 'generic constructions' in model theory. Some, like structures with generic predicates, or algebraically closed fields with several independent valuations, are explicitly interpolative fusions, while others, like structures with generic automorphisms, or fields with generic operators, are bi-interpretable with interpolative fusions. In joint work with Erik Walsberg and Minh Tran, we study two basic questions: (1) When does the interpolative fusion exist, and how can we axiomatize it? (2) How can we understand properties of the interpolative fusion T* in terms of properties of the theories T, T', and their intersection?
Next Week in Logic at CUNY:
- - - - Monday, Nov 25, 2019 - - - -
Logic and Metaphysics Workshop Date: Monday, November 11, 4.15-6.15 Place: Room 7314, CUNY Graduate Center
Vincent Alexis Peluce (CUNY) Title: Memory and Intuitionistic Logic
Abstract: L.E.J. Brouwer writes, “people try by means of sounds and symbols to originate in other people copies of the mathematical constructions and reasonings which they have made themselves; by the same means they try to aid their own memory. In this way the mathematical language comes into being, and as its special case the language of logical reasoning” (1907). More is left to be said, however, about the relation between the Brouwerian subject and logical language. In this talk we discuss the usual account of this relation and some problems with that view. We then propose an alternative.
- - - - Tuesday, Nov 26, 2019 - - - -
- - - - Wednesday, Nov 27, 2019 - - - -
The New York City Category Theory Seminar Department of Computer Science, Department of Mathematics The Graduate Center of The City University of New York
Speaker: James Myer Date and Time: Wednesday November 27, 2019, 7:00 - 8:30 PM., Room 6417.
Title: Higher-Order Categorical Logic: TBA.
Abstract: We will be starting at 0.6 and go forward.
This week, Vinicius Rodrigues of the University of São Paulo will speak in the seminar. His talk is entitled "Psi spaces with pseudocompact hyperspaces."
Abstract: The Hyperspace of Vietoris of a topological space X is a topology given to the space of nonempty closed subsets of X. A famous theorem due to Vietoris states that X is compact iff its hyperspace is compact, so the natural question of whether there are other relations between the two spaces with respect to notions that generalize compactness arise. J. Ginsburg has asked whether for a space X, X^omega pseudocompact implies that the hyperspace of X is pseudocompact. A negative answer was given by M. Hrusak, I. Martinez-Ruiz, and F. Hernandez-Hernandez. They also studied this question restricted to psi spaces of MAD families, and, restricted to these psi spaces, the answer is independent of ZFC. However, it is not known if, in ZFC, there exists a MAD family whose psi space has pseudocompact hyperspace. V. Rodrigues and A. Tomita showed that it is consistent that there exists two MAD families, one whose psi space has pseudocompact hyperspace, and one whose psi space hasn't.
The talk will be held on Friday, November 22 in Fields 210 from 1:30 to 3:30. If you will attend the talk, please register using the following link:
Please make note to change the date to the date of the seminar (November 22) for registration.
Thanks!
Bill
(KGRC) upcoming talks in the research seminar
Kurt Godel Research Center
11/18/2019
The KGRC welcomes as guests:
Jana Marikova (host: Benjamin Miller) will stay until June 30, 2020.
Clifton Ealy (host: Benjamin Miller) will stay until January 11, then
visit again March 7 to March 15 and May 9 to June 30.
Sarka Stejskalova (host: Sy-David Friedman) will stay from November 21 to
November 22.
Radek Honzik (host: Sy-David Friedman) will stay from November 21 to
November 22.
Istvan Juhasz (host: Sy-David Friedman) will stay from November 25 to
December 1 and give a talk on November 28 (see below).
Miguel Moreno (host: Lyubomyr Zdomskyy) will stay from December 1, 2019 to
November 30, 2020 and give a talk on January 23.
Mohammad Golshani (hosts: Sy-David Friedman, Yair Hayut) will stay from
December 4 to December 11 and give a talk on December 5.
Oleksandr Ravsky (host: Lyubomyr Zdomskyy) will stay from December 9 to
December 22 and give a talk on December 12.
Taras Banakh (host: Lyubomyr Zdomskyy) will stay from December 17 to
January 3 and give a talk (talk to be confirmed).
Jaroslav Supina (host: Vera Fischer) will stay from January 8 to January
10 and give a talk on January 9.
Corey Switzer (host: Vera Fischer) will stay from January 12 to January 19
and give a talk on January 16.
Chi Tat Chong (host: Sy-David Friedman) will give a talk on June 18, 2020.
* * *
Research seminar
Kurt Gödel Research Center
Thursday, November 21
"Cichon's Maximum without large cardinals"
Martin Goldstern (TU Wien)
How many Lebesgue null sets are needed to cover the real line? How many
functions (from the natural numbers to the natural numbers) are needed to
dominate all functions? The answers to these questions and 10 more related
questions are certain uncountable cardinals collected in Cichon's Diagram,
which also shows provable inequalities between these cardinals.
In a recent joint work with Jakob Kellner, Diego Mejia and Saharon Shelah,
we constructed a model where the cardinals in Cichon's Diagram have 10
different values (which is known to be best possible).
The construction first uses a finite support iteration P to get 5
different values for the left side of the diagram, and then finds a subset
P' which also separates the values on the right side.
Time and Place
Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47)
Talk at 4:00pm in the KGRC lecture room (seminar room D5.48)
Universität Wien
Institut für Mathematik
Kurt Gödel Research Center
Augasse 2-6, UZA 1 - Building 2
1090 Wien
* * *
Research seminar
Kurt Gödel Research Center
Thursday, November 28
"Large cardinals in topology"
Istvan Juhasz
(Renyi Mathematical Institute, Budapest, Hungary)
In this talk I intend to deal with a number of problems of general
topology that, sometimes rather naturally but sometimes quite
surprisingly, lead to or boil down to statements of set theory involving
various large cardinals.
Time and Place
Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47)
Talk at 4:00pm in the KGRC lecture room (seminar room D5.48)
Universität Wien
Institut für Mathematik
Kurt Gödel Research Center
Augasse 2-6, UZA 1 - Building 2
1090 Wien
Tagged: Martin Goldstern, István Juhász
Logic and Set Theory Seminar: November 19, 3:00 - 3:50 pm
Boise Logic and Set Theory Seminar
11/18/2019
Colleagues,
The speaker for the next meeting of the Fall 2019 Logic and Set Theory seminar is Dr. Randall Holmes of the Department of Mathematics. Details are as follows:
Location: Mathematics Building Room 124
Date/time: Tuesday, November 19, 3:00 - 3:50 pm
Title: The axiom of cantorian sets in NFU and the existence of n-Mahlo cardinals - PART 2
Abstract: We report on some observations of Robert Solovay, somewhat extended and refined by the speaker, regarding the relationship between the seemingly innocent Axiom of Cantorian Sets proposed by C Ward Henson for NF a long time ago, and the existence of n-Mahlo cardinals. A partition theorem of Schmerl will be described which handles the relationship in one direction.
Regards,
Marion Scheepers
Distinguished Professor
Department of Mathematics
Boise State University
Boise, ID 83725
U.S.A.
This Week in Logic at CUNY
This Week in Logic at CUNY
11/17/2019
This Week in Logic at CUNY:
- - - - Monday, Nov 18, 2019 - - - -
Logic and Metaphysics Workshop Date: Monday, November 11, 4.15-6.15 Place: Room 7314, CUNY Graduate Center Matías Bulnes (CUNY)
Title: An Unorthodox Solution to the Hintikka-Kripke Problem
Abstract: The Hintikka-Kripke problem consists in reconciling Hintikka’s semantics for doxastic operators and Kripke’s semantics for alethic operators. The problem arises from their treatment of identity. While the necessity of identities was one of the main innovations of Kripke’s semantics, Hintikka needs identities to be contingent to explain the opacity of doxastic operators. Yet alethic and doxastic operators are combined effortlessly in everyday discourse. In the talk, I will first discuss various attempts at reconciliation within the orthodoxy about opacity, and raise objections to them. Then, I will propose an unorthodox idea: rather than thinking of doxastic operators as introducing new possible worlds with different identities, think of them as introducing new logical spaces with different domains of objects. This achieves reconciliation by circumscribing the necessity of identities to the logical space of each agent. To assess this idea viz-a-viz its competitors, we will have to reexamine some fundamental concepts of the problem of opacity, such as the concepts of language and semantics.
- - - - Tuesday, Nov 19, 2019 - - - -
- - - - Wednesday, Nov 20, 2019 - - - -
Computational Logic Seminar Time 2:00 - 4:00 PM, Room 5382 Tuesday, November 19 Speaker: Sergei Artemov, CUNY Graduate Center Title: On Logical Foundations of Strategic Games II
Abstract: In his dissertation of 1950, Nash based his concept of the solution to a game on the assumption that “a rational prediction should be unique, that the players should be able to deduce and make use of it”. We study when such definitive solutions exist for strategic games with ordinal payoffs. We show that games without Nash equilibria do not have definitive solutions under any notion of rationality, but each Nash equilibrium can be a definitive solution for an appropriate refinement of Aumann rationality. With respect to Aumann rationality itself, games with multiple Nash equilibria cannot have definitive solutions. Some games with a unique Nash equilibrium have definitive solutions, others don’t, and the criterion for a definitive solution is provided by the iterated deletion of strictly dominated strategies.
The New York City Category Theory Seminar Department of Computer Science, Department of Mathematics The Graduate Center of The City University of New York
Speaker: Raymond Puzio. Date and Time: Wednesday November 20, 2019, 7:00 - 8:30 PM., Room 6417. Title: Posets, Lifting properties, and Completions.
Abstract: Ever since Dedekind, it has been known that special classes of posets can be characterized in terms of forbidden configurations. We note how these characterizations result from lifting properties which, in turn, correspond to propositions in regular logic. This leads us to consider subcategories of morphisms between posets and idempotent completions.
- - - - Thursday, Nov 21, 2019 - - - -
- - - - Friday, Nov 22, 2019 - - - -
Set Theory Seminar CUNY Graduate Center, Room 6417 Friday, November 22, 10:00-11:45am
Brent Cody, Virginia Commonwealth University A refinement of the Ramsey hierarchy via indescribability
A subset XX of a cardinal κκ is Ramsey if for every function f:[X]<ωo2f:[X]<ωo2 there is a set H⊆XH⊆X of cardinality κκ which is homogeneous for ff, meaning that f↾[H]nf↾[H]n is constant for each n<ωn<ω. Baumgartner proved that if κκ is Ramsey, then the collection of non-Ramsey subsets of κκ is a normal ideal on κκ. We will discuss some recent results concerning Ramsey properties in which homogeneous sets are demanded to be indescribable of a particular degree. Moreover, by iterating Feng's Ramsey operator, which he used to define a notion of αα-Ramseyness of a cardinal κκ, we will consider hypotheses in which homogeneous sets themselves satisfy various Ramsey properties. For ordinals α,β<κα,β<κ we will define a notion of αα-Π1βΠβ1-Ramseyness of a cardinal κκ where αα indicates how many times the Ramsey operator has been iterated and ββ indicates the degree of transfinite indescribability (due to Sharpe-Welch and independently Bagaria) one initially demands homogeneous to satisfy. We will prove that for α,β<κα,β<κ an αα-Π1βΠβ1-Ramsey cardinal is strictly between Feng's αα-Ramsey and an (α+1α+1)-Ramsey cardinal in consistency strength. Moreover, for fixed α<κα<κ, as ββ increases the αα-Π1βΠβ1-Ramsey cardinals yield a strictly increasing hierarchy, in a somewhat subtle sense. For β0<β1<κβ0<β1<κ and for large enough α<κα<κ, κκ being αα-Π1β0Πβ01-Ramsey is equivalent to κκ being αα-Π1β1Πβ11-Ramsey (we will identify the least αα at which this equivalence occurs). But if α,β0<κα,β0<κ there is a large enough β1<κβ1<κ such that κκ being αα-Π1β0Πβ01-Ramsey is strictly weaker than κκ being αα-Π1β1Πβ11-Ramsey. All of these results seem to require a careful analysis of the ideals associated to the various large cardinal notions.
Model Theory Seminar
CUNY Graduate Center, Room 6417
Friday, November 22, 12:30-2:00pm
Alex Kruckman, Wesleyan University A diversity of Kim's Lemmas
One of the most important steps in the development of simplicity theory by Kim and Pillay in the 1990s was a result now known as Kim's Lemma: In a simple theory, if a formula divides, then this dividing is witnessed by every Morley sequence in the appropriate type. More recently, variants on Kim's Lemma have been shown (by Chernikov, Kaplan, and Ramsey) to follow from, and in fact characterize, the combinatorial dividing lines NTP2 and NSOP1: two generalizations of simplicity in different directions. After surveying the Kim's Lemmas of the past, I will speculate about a new combinatorial dividing line, generalizing both NTP2 and NSOP1 and characterized by a new variant of Kim's Lemma. This is joint speculation with Nick Ramsey.
Logic Workshop CUNY Graduate Center, Room 6417 Friday, November 22, 2:00-3:30pm
Alex Kruckman, Wesleyan University Interpolative fusions
Fix languages L and L' (possibly non-disjoint). An structure M in the union of these languages is interpolative if whenever X is an L-definable set in M and X' is an L'-definable set in M, X and X' intersect unless they are separated by disjoint definable sets in the intersection of L and L'. When T is an L theory and T' is an L' theory, we say that a theory T* is the interpolative fusion of T and T' if it axiomatizes the class of interpolative models of the union of T and T'. If T and T' are model-complete, this is exactly the model companion of the union theory. Interpolative fusions provide a unified framework for studying many examples of 'generic constructions' in model theory. Some, like structures with generic predicates, or algebraically closed fields with several independent valuations, are explicitly interpolative fusions, while others, like structures with generic automorphisms, or fields with generic operators, are bi-interpretable with interpolative fusions. In joint work with Erik Walsberg and Minh Tran, we study two basic questions: (1) When does the interpolative fusion exist, and how can we axiomatize it? (2) How can we understand properties of the interpolative fusion T* in terms of properties of the theories T, T', and their intersection?
Next Week in Logic at CUNY:
- - - - Monday, Nov 25, 2019 - - - -
Logic and Metaphysics Workshop Date: Monday, November 11, 4.15-6.15 Place: Room 7314, CUNY Graduate Center
Vincent Alexis Peluce (CUNY) Title: Memory and Intuitionistic Logic
Abstract: L.E.J. Brouwer writes, “people try by means of sounds and symbols to originate in other people copies of the mathematical constructions and reasonings which they have made themselves; by the same means they try to aid their own memory. In this way the mathematical language comes into being, and as its special case the language of logical reasoning” (1907). More is left to be said, however, about the relation between the Brouwerian subject and logical language. In this talk we discuss the usual account of this relation and some problems with that view. We then propose an alternative.
- - - - Tuesday, Nov 26, 2019 - - - -
- - - - Wednesday, Nov 27, 2019 - - - -
The New York City Category Theory Seminar Department of Computer Science, Department of Mathematics The Graduate Center of The City University of New York
Speaker: TBA Date and Time: Wednesday November 27, 2019, 7:00 - 8:30 PM., Room 6417.
Title: Higher-Order Categorical Logic: TBA.
Abstract: We will be starting at TBA and go forward.
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Wednesday seminar
Prague Set Theory Seminar
11/14/2019
PS: I just noticed this announcement:
http://www.math.cas.cz/documents/cech16.pdf
Stevo Todorcevic will deliver a distinguished lecture on Tuesday
December 3rd 2019 at 10:30 in the Institute of Mathematics CAS.
Best,
David
On 14/11/2019 09:50, David Chodounsky wrote:
> Dear all,
>
> The seminar meets on Wednesday November 20th at 11:00 in the Institute
> of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
>
> Program: Osvaldo Guzman -- The splitting and the ultrafilter numbers
>
> Blass and Shelah showed that it is consistent that the ultrafilter
> number is smaller than the splitting number. In this talk, we will
> provide a different proof that this inequality is consistent. This is a
> part of a joint work with Damjan Kalajdzievski.
>
>
>
> Best,
> David
Wednesday seminar
Prague Set Theory Seminar
11/14/2019
Dear all,
The seminar meets on Wednesday November 20th at 11:00 in the Institute
of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Osvaldo Guzman -- The splitting and the ultrafilter numbers
Blass and Shelah showed that it is consistent that the ultrafilter
number is smaller than the splitting number. In this talk, we will
provide a different proof that this inequality is consistent. This is a
part of a joint work with Damjan Kalajdzievski.
Best,
David
Set theory seminar this Friday
Toronto Set Theory Seminar
11/12/2019
Hi everyone,
We will have Jan Pachl speaking in the seminar this week about DTC ultrafilters on groups.
Abstract: An infinite finitely generated group G is virtually abelian if and only if it does not admit a DTC ultrafilter = an ultrafilter that determines the topological centre of the semigroup βG. More generally, we have necessary conditions and, for countable groups, sufficient conditions for the existence of DTC ultrafilters. This is joint work with Juris Steprans.
The talk will be held on Friday, November 15 in Fields 210 from 1:30 to 3:30. If you will attend the talk, please register using the following link:
Place: Fields Institute (Room 210)
Date: November 1, 2019 (13:30-15:00)
Speaker: Juris Steprans
Title: A model where
(KGRC) talk in the research seminar Thursday, November 14
Kurt Godel Research Center
11/11/2019
The KGRC welcomes as guests:
Jana Marikova (host: Benjamin Miller) will stay until June 30, 2020.
Clifton Ealy (host: Benjamin Miller) will stay until January 11, 2020,
then visit again March 7 to March 15 and May 9 to June 30.
Sarka Stejskalova (host: Sy-David Friedman) will stay from November 21 to
November 22.
Radek Honzik (host: Sy-David Friedman) will stay from November 21 to
November 22.
Istvan Juhasz (host: Sy-David Friedman) will stay from November 25 to
December 1 and give a talk on November 28.
Miguel Moreno (host: Lyubomyr Zdomskyy) will stay from December 1, 2019 to
November 30, 2020 and give a talk on January 23.
Mohammad Golshani (hosts: Sy-David Friedman, Yair Hayut) will stay from
December 4 to December 11 and give a talk on December 5.
Oleksandr Ravsky (host: Lyubomyr Zdomskyy) will stay from December 9 to
December 22 and give a talk on December 12.
Taras Banakh (host: Lyubomyr Zdomskyy) will stay from December 17, 2019 to
January 3, 2020 and give a talk (talk to be confirmed).
Jaroslav Supina (host: Vera Fischer) will give a talk on January 9, 2020.
Corey Switzer (host: Vera Fischer) will stay from January 12, 2020 to
January 19, 2020 and give a talk on January 16.
Chi Tat Chong (host: Sy-David Friedman) will give a talk on June 18, 2020.
* * *
Research seminar
Kurt Gödel Research Center
Thursday, November 14
"L[Reg]"
Sy-David Friedman (KGRC)
Gitik and I showed that L[Reg], like L[Card] and V, is a forcing extension
of an iterate of a mouse. For L[Card] the mouse is the least one with a
measurable limit of measurables (result of Philip Welch) and for V it's
Mighty Mouse. For L[Reg] it's the least mouse with a measure concentrating
on measurables, but the iterate may have to be truncated (for example if
there are no regular limit cardinals). We use Magidor's iteration of
Prikry forcings. An unexpected twist is that we need to use old-fashioned
mice and not fine-structural mice for the proof.
Time and Place
Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47)
Talk at 4:00pm in the KGRC lecture room (seminar room D5.48)
Universität Wien
Institut für Mathematik
Kurt Gödel Research Center
Augasse 2-6, UZA 1 - Building 2
1090 Wien
Logic and Set Theory Seminar: November 12, 3:00 - 3:50 pm
Boise Logic and Set Theory Seminar
11/11/2019
Colleagues,
The speaker for the next two meetings of the Fall 2019 Logic and Set Theory seminar is Dr. Randall Holmes of the Department of Mathematics. Details are as follows:
Location: Mathematics Building Room 124
Date/time: Tuesday, November 12, 3:00 - 3:50 pm
Title: The axiom of cantorian sets in NFU and the existence of n-Mahlo cardinals
Abstract: We report on some observations of Robert Solovay, somewhat extended and refined by the speaker, regarding the relationship between the seemingly innocent Axiom of Cantorian Sets proposed by C Ward Henson for NF a long time ago, and the existence of n-Mahlo cardinals. A partition theorem of Schmerl will be described which handles the relationship in one direction.
Regards,
Marion
Distinguished Professor
Department of Mathematics
Boise State University
Boise, ID 83725
U.S.A.
This Week in Logic at CUNY
This Week in Logic at CUNY
11/10/2019
This Week in Logic at CUNY:
- - - - Monday, Nov 11, 2019 - - - -
Logic and Metaphysics Workshop Date: Monday, November 11, 4.15-6.15 Place: Room 7314, CUNY Graduate Center
Martin Pleitz (Hamburg) Title: Talking about Reification
Abstract: Reification is the systematic association of a non-object with an object that encodes it. Therefore the reificationist must be a trans-objectist – i.e., anyone who thinks that there are instances of reification must also think that some items are not objects. As exemplified by Frege’s puzzle of the concept horse, non-objects and reification are notoriously difficult to talk about. Therefore I will begin my presentation by outlining a formal language that enables the trans-objectist and the reificationist to speak in a way that is not self-undermining. I will go on and employ the framework to give a uniform diagnosis of the set theoretic and semantic paradoxes in terms of static reification that is an alternative to Graham Priest’s Inclosure Schema, and sketch how dynamic reification can provide a uniform solution to the paradoxes as well as a general account of the constitution of abstract objects. In order to achieve this it will be crucial to import some tools of Procedural Postulationism, a dynamic account of the ontology of mathematics developed by Kit Fine.
- - - - Tuesday, Nov 12, 2019 - - - -
Computational Logic Seminar Tuesday, November 12, Time 2:00 - 4:00 PM, Room 5382 Speaker: Sergei Artemov, CUNY Graduate Center Title: On Logical Foundations of Strategic Games
Abstract: In his dissertation of 1950, Nash based his concept of the solution to a game on the assumption that “a rational prediction should be unique, that the players should be able to deduce and make use of it”. We study when such definitive solutions exist for strategic games with ordinal payoffs. We offer a new, syntactic approach: instead of reasoning about the specific model of a game, we deduce properties of interest directly from the description of the game itself. This captures Nash’s deductive assumptions and helps to bridge a well-known gap between syntactic game descriptions and specific models which could require unwarranted additional epistemic assumptions, e.g., common knowledge of a model. We show that games without Nash equilibria do not have definitive solutions under any notion of rationality, but each Nash equilibrium can be a definitive solution for an appropriate refinement of Aumann rationality. With respect to Aumann rationality itself, games with multiple Nash equilibria cannot have definitive solutions. Some games with a unique Nash equilibrium have definitive solutions, others don’t, and the criterion for a definitive solution is provided by the iterated deletion of strictly dominated strategies.
- - - - Wednesday, Nov 13, 2019 - - - -
The New York City Category Theory Seminar Department of Computer Science, Department of Mathematics The Graduate Center of The City University of New York
Date and Time: Wednesday November 13, 2019, 7:00 - 8:30 PM., Room 6417. Speaker: James Myer. Title: Higher-Order Categorical Logic: Limits. Abstract: We will be starting at Section 0.5 and go forward.
- - - - Thursday, Nov 14, 2019 - - - -
- - - - Friday, Nov 15, 2019 - - - -
Model Theory Seminar
NOTE SPECIAL TIME: 10:00-11:30am
CUNY Graduate Center, Room 6417
November 15
Andrés Villaveces, Universidad Nacional de Colombia TBA
Set Theory Seminar
NOTE SPECIAL TIME: 12:30-2:00pm
CUNY Graduate Center, Room 6417
Friday, November 15
Dominik Adolf, Bar-Ilan University Constructing (PCF)-scales through a covering argument
We will present a method of constructing scales on products of regular cardinals. The choice of cardinals depends on the position of 'cutpoints' in the extender sequence of the core model. Here we will only discuss the simplest case of sequences of measures. Scale degrees will correspond to structures occurring in K that will be familiar to some from the construction of square sequences (both global and local) in fine structural inner models. The scale so constructed is canonical, short, and otherwise nice. This work is part of a joint project with Omer Ben-Neria.
Logic Workshop CUNY Graduate Center, Room 6417 Friday, September 15, 2:00-3:30pm
Sandra Müller, University of Vienna Infinite decreasing chains in the Mitchell order
It is known that the behavior of the Mitchell order substantially changes at the level of rank-to-rank extenders, as it ceases to be well-founded. While the possible partial order structure of the Mitchell order below rank-to-rank extenders is considered to be well understood, little is known about the structure in the ill-founded case. We make a first step in understanding this case by studying the extent to which the Mitchell order can be ill-founded. Our main results are (i) in the presence of a rank-to-rank extender there is a transitive Mitchell order decreasing sequence of extenders of any countable length, and (ii) there is no such sequence of length ω1. This is joint work with Omer Ben-Neria.
Next Week in Logic at CUNY:
- - - - Monday, Nov 18, 2019 - - - -
Logic and Metaphysics Workshop Date: Monday, November 11, 4.15-6.15 Place: Room 7314, CUNY Graduate Center Matías Bulnes (CUNY)
Title: An Unorthodox Solution to the Hintikka-Kripke Problem
Abstract: The Hintikka-Kripke problem consists in reconciling Hintikka’s semantics for doxastic operators and Kripke’s semantics for alethic operators. The problem arises from their treatment of identity. While the necessity of identities was one of the main innovations of Kripke’s semantics, Hintikka needs identities to be contingent to explain the opacity of doxastic operators. Yet alethic and doxastic operators are combined effortlessly in everyday discourse. In the talk, I will first discuss various attempts at reconciliation within the orthodoxy about opacity, and raise objections to them. Then, I will propose an unorthodox idea: rather than thinking of doxastic operators as introducing new possible worlds with different identities, think of them as introducing new logical spaces with different domains of objects. This achieves reconciliation by circumscribing the necessity of identities to the logical space of each agent. To assess this idea viz-a-viz its competitors, we will have to reexamine some fundamental concepts of the problem of opacity, such as the concepts of language and semantics.
- - - - Tuesday, Nov 19, 2019 - - - -
- - - - Wednesday, Nov 20, 2019 - - - -
The New York City Category Theory Seminar Department of Computer Science, Department of Mathematics The Graduate Center of The City University of New York
Speaker: Raymond Puzio. Date and Time: Wednesday November 20, 2019, 7:00 - 8:30 PM., Room 6417. Title: Posets, Lifting properties, and Completions.
Abstract: Ever since Dedekind, it has been known that special classes of posets can be characterized in terms of forbidden configurations. We note how these characterizations result from lifting properties which, in turn, correspond to propositions in regular logic. This leads us to consider subcategories of morphisms between posets and idempotent completions.
- - - - Thursday, Nov 21, 2019 - - - -
- - - - Friday, Nov 22, 2019 - - - -
Set Theory Seminar CUNY Graduate Center, Room 6417 Friday, November 22, 10:00-11:45am
Brent Cody, Virginia Commonwealth University A refinement of the Ramsey hierarchy via indescribability
A subset XX of a cardinal κκ is Ramsey if for every function f:[X]<ωo2f:[X]<ωo2 there is a set H⊆XH⊆X of cardinality κκ which is homogeneous for ff, meaning that f↾[H]nf↾[H]n is constant for each n<ωn<ω. Baumgartner proved that if κκ is Ramsey, then the collection of non-Ramsey subsets of κκ is a normal ideal on κκ. We will discuss some recent results concerning Ramsey properties in which homogeneous sets are demanded to be indescribable of a particular degree. Moreover, by iterating Feng's Ramsey operator, which he used to define a notion of αα-Ramseyness of a cardinal κκ, we will consider hypotheses in which homogeneous sets themselves satisfy various Ramsey properties. For ordinals α,β<κα,β<κ we will define a notion of αα-Π1βΠβ1-Ramseyness of a cardinal κκ where αα indicates how many times the Ramsey operator has been iterated and ββ indicates the degree of transfinite indescribability (due to Sharpe-Welch and independently Bagaria) one initially demands homogeneous to satisfy. We will prove that for α,β<κα,β<κ an αα-Π1βΠβ1-Ramsey cardinal is strictly between Feng's αα-Ramsey and an (α+1α+1)-Ramsey cardinal in consistency strength. Moreover, for fixed α<κα<κ, as ββ increases the αα-Π1βΠβ1-Ramsey cardinals yield a strictly increasing hierarchy, in a somewhat subtle sense. For β0<β1<κβ0<β1<κ and for large enough α<κα<κ, κκ being αα-Π1β0Πβ01-Ramsey is equivalent to κκ being αα-Π1β1Πβ11-Ramsey (we will identify the least αα at which this equivalence occurs). But if α,β0<κα,β0<κ there is a large enough β1<κβ1<κ such that κκ being αα-Π1β0Πβ01-Ramsey is strictly weaker than κκ being αα-Π1β1Πβ11-Ramsey. All of these results seem to require a careful analysis of the ideals associated to the various large cardinal notions.
Logic Workshop CUNY Graduate Center, Room 6417 Friday, September 22, 2:00-3:30pm
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Logic Seminar 14 Nov 2019 17:00 hrs at NUS by Thilo Weinert
NUS Logic Seminar
11/7/2019
Invitation to the Logic Seminar at the National University of Singapore
Date: Thursday, 14 November 2019, 17:00 hrs
Room: S17#06-11, Department of Mathematics, NUS
Speaker: Thilo Weinert
Title: Partition Relations for Linear Orders in a Choiceless Context
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: Most Partition Relations are proved for Ordinals, not
general linear orders. This is due to the Axiom of Choice which I will
consequently ignore during most of the lecture. Some exceptions to the
rule mentioned at the beginning can be found in a 1971 paper by
Erdoes, Milner and Rado and I will present some analogous results
for linear orders which are given rise to by lexicographically
ordered sequences of zeros and ones. I will close by discussing an
open problem in this context.
This is joint work (from a few years back) with Philipp Luecke and
Philipp Schlicht, the url of the article in the Springer proceedings is
https://link.springer.com/article/10.1007/s11083-016-9405-0
UPDATE: This Week in Logic at CUNY
This Week in Logic at CUNY
11/7/2019
Hi everyone,
Please note that Friday's (tomorrow's) talk in the Seminar in Logic, Games and Language by Prof. Rohit Parikh has been postponed. Updated information will be distributed in future mailings.
Best,
Jonas
This Week in Logic at CUNY:
- - - - Monday, Nov 4, 2019 - - - -
Logic and Metaphysics Workshop Date: Monday, November 4, 4.15-6.15 Place: Room 7314, CUNY Graduate Center Speaker: Sergei Artemov (CUNY)
Title: The Provability of Consistency
Abstract: We revisit the foundational question “Can consistency of a theory T be established by means of T?” The usual answer “No, by Gödel’s Second Incompleteness Theorem” is based on two assumptions:
1. Gödel’s internalized consistency formula is the only way to represent consistency. 2. Any contentual reasoning within T internalizes as a formal derivation in T.
We show that already for Peano arithmetic PA both of these assumptions are false: (1) does not cover such legitimate mode of presentation as schemes (think of the Induction scheme), (2) fails for schemes. Based on these observations, we offer a proof of PA-consistency by means of PA and discuss its potential impact.
- - - - Tuesday, Nov 5, 2019 - - - -
Computational Logic Seminar Time 2:00 - 4:00 PM, Room 5382 Tuesday, November 5 Speaker: Sergei Artemov, CUNY Graduate Center Title: On Aggregating Probabilistic Evidence
Abstract: Imagine a database -- a set of propositions S={F_1,F_2,…,F_n} with some kind of probability estimates and let a proposition X logically follow from S. What is the best lower bound of the probability of X? The traditional approach computes a crude numeric lower bound for X from probabilities of F_i's corresponding to a worst-case configuration.
We suggest a more flexible parameterized approach by assuming probability events u_1,u_2,…,u_n which are evidence for F_1,F_2,…,F_n, and calculating “aggregated evidence” e(u_1,u_2,…,u_n) for X. The probability of e provides a tight lower bound for any, not only a worst-case, situation. This model is formalized in Justification Logic and supported by corresponding completeness theorems. With this approach, one can handle conflicting and inconsistent data and gather both positive and negative evidence for the same proposition.
- - - - Wednesday, Nov 6, 2019 - - - -
MOPA (Models of Peano Arithmetic) CUNY Graduate Center, Room 4213.03 (Math Thesis Room) Wednesday, November 6, 6:30-8:00pm Roman Kossak, CUNY Short recursively saturated models of PA as an AEC
Countable short recursively saturated models of PA can serve as bases for abstract elementary classes that are complete but not irreducible. I will explain all these notions and show the construction.
The New York City Category Theory Seminar Department of Computer Science Department of Mathematics The Graduate Center of The City University of New York
Speaker: Dan Shiebler, Oxford. Date and Time: Wednesday November 6, 2019, 7:00 - 8:30 PM., Room 6417. Title: Incremental Monoidal Categories for Speech.
Abstract: In some systems new information is incrementally introduced. For example, each new word in spoken speech modifies the structure and content of a sentence. Although monoidal categories are a popular foundation for linguistic modeling, they are not natively equipped with structure to model incrementality along the tensor-product dimension. In this work we present a characterization of formal grammars as monoidal categories, which we call monoidal grammars. We also characterize automata that parse formal grammars as F-coalgebras. We use these characterizations to derive a functor from the category of monoidal grammars to the category of F-coalgebras.
- - - - Thursday, Nov 7, 2019 - - - -
- - - - Friday, Nov 8, 2019 - - - -
Set Theory Seminar CUNY Graduate Center, Room 6417 Friday, November 8, 10:00-11:45am
Iian Smythe, Rutgers University Parametrized diamonds and mad families of subspaces
In their 2004 paper, Moore, Hrusak and Dzamonja isolated a weakening of Jensen's diamond principle that could be 'parametrized' by a cardinal invariant, implies that the corresponding invariant is small, and yet is consistent with the failure of the Continuum Hypothesis. Moreover, these principles fully determine many cardinal invariants in 'canonical' models, those obtained by iterations of definable proper forcings. I will give a survey of this subject, and then describe a recent application in the study of maximal almost disjoint families of subspaces of a countably infinite-dimensional vector space.
THE FOLLOWING TALK HAS BEEN POSTPONED:
Seminar in Logic, Games and Language Friday, November 8, 2019, 4:15 PM, room 4421 Rohit Parikh, Brooklyn College and CUNY Graduate Center Finite and Infinite Dialogues
Next Week in Logic at CUNY:
- - - - Monday, Nov 11, 2019 - - - -
Logic and Metaphysics Workshop Date: Monday, November 11, 4.15-6.15 Place: Room 7314, CUNY Graduate Center
Martin Pleitz (Hamburg) Title: Talking about Reification
Abstract: Reification is the systematic association of a non-object with an object that encodes it. Therefore the reificationist must be a trans-objectist – i.e., anyone who thinks that there are instances of reification must also think that some items are not objects. As exemplified by Frege’s puzzle of the concept horse, non-objects and reification are notoriously difficult to talk about. Therefore I will begin my presentation by outlining a formal language that enables the trans-objectist and the reificationist to speak in a way that is not self-undermining. I will go on and employ the framework to give a uniform diagnosis of the set theoretic and semantic paradoxes in terms of static reification that is an alternative to Graham Priest’s Inclosure Schema, and sketch how dynamic reification can provide a uniform solution to the paradoxes as well as a general account of the constitution of abstract objects. In order to achieve this it will be crucial to import some tools of Procedural Postulationism, a dynamic account of the ontology of mathematics developed by Kit Fine.
- - - - Tuesday, Nov 12, 2019 - - - -
- - - - Wednesday, Nov 13, 2019 - - - -
- - - - Thursday, Nov 14, 2019 - - - -
- - - - Friday, Nov 15, 2019 - - - -
Set Theory Seminar CUNY Graduate Center, Room 6417
Friday, November 15, 10:00-11:45am
Dominik Adolf, Bar-Ilan University Constructing (PCF)-scales through a covering argument
We will present a method of constructing scales on products of regular cardinals. The choice of cardinals depends on the position of 'cutpoints' in the extender sequence of the core model. Here we will only discuss the simplest case of sequences of measures. Scale degrees will correspond to structures occurring in K that will be familiar to some from the construction of square sequences (both global and local) in fine structural inner models. The scale so constructed is canonical, short, and otherwise nice. This work is part of a joint project with Omer Ben-Neria.
Logic Workshop CUNY Graduate Center, Room 6417 Friday, September 15, 2:00-3:30pm
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If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Wednesday seminar
Prague Set Theory Seminar
11/6/2019
Dear all,
The seminar meets on Wednesday November 13th at 11:00 in the Institute
of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
(Another event, Dny otevrenych dveri will take place in the Institute at
the same time, but the seminar should take place the same way as usual.)
Program: Osvaldo Guzman -- The ultrafilter number and the almost
disjointness number
In this talk, we will prove that every MAD family can be destroyed by a
proper forcing that does not add dominating reals and preserves
P-points. In particular, we can get a model of omega_1=u < a. This
answers questions of Brendle and Shelah.
Best,
David
Logic Seminar 7 Nov 2019 17:00 hrs at NUS - The work of Gerald Sacks
NUS Logic Seminar
11/6/2019
Invitation to the Logic Seminar at the National University of Singapore
Date: Thursday, 7 November 2019, 17:00 hrs
Room: S17#06-11, Department of Mathematics, NUS
Speaker: Chong Chi Tat
Title: The work of Geral Sacks
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Gerald E Sacks (1933--2019) completed his thesis under Barkley Rosser
at Cornell. He was a visitor at the Institute for Advanced Study in
Princeton and a faculty member at Cornell. He subsequently moved to MIT
and then took up a joint appointment as Professor of Mathematical Logic
at Harvard. Sacks did pioneering work in recursion theory and higher
recursion theory and made fundamental contributions to logic. This talk
will give a sypnosis of what we think to be Sacks' most significant
achievements, and the impact of his work on the development of logic.
Some recollection of Sacks as a person will also be sprinkled during the talk.
(KGRC) talk in the research seminar Thursday, November 7
Kurt Godel Research Center
11/4/2019
The KGRC welcomes as guests:
Jana Marikova (host: Benjamin Miller) will stay util June 30, 2020 and
give a talk on November 7 (see below).
Clifton Ealy (host: Benjamin Miller) will stay until June 30, 2020.
Sarka Stejskalova (host: Sy-David Friedman) will stay from November 21 to
November 22.
Radek Honzik (host: Sy-David Friedman) will stay from November 21 to
November 22.
Istvan Juhasz (host: Sy-David Friedman) will stay from November 25 to
December 1 and give a talk on November 28.
Miguel Moreno (host: Lyubomyr Zdomskyy) will stay from December 1, 2019 to
November 30, 2020 and give a talk on January 23.
Mohammad Golshani (hosts: Sy-David Friedman, Yair Hayut) will stay from
December 4 to December 11 and give a talk on December 5.
Oleksandr Ravsky (host: Lyubomyr Zdomskyy) will stay from December 9 to
December 22 and give a talk on December 12.
Taras Banakh (host: Lyubomyr Zdomskyy) will stay from December 17, 2019 to
January 3, 2020 and give a talk (talk to be confirmed).
Jaroslav Supina (host: Vera Fischer) will give a talk on January 9, 2020.
Corey Switzer (host: Vera Fischer) will stay from January 12, 2020 to
January 19, 2020 and give a talk on January 16.
Chi Tat Chong (host: Sy-David Friedman) will give a talk on June 18, 2020.
* * *
Research seminar
Kurt Gödel Research Center
Thursday, November 7
"Measures and o-minimal structures"
Jana Marikova
(Western Illinois University, Macomb, USA)
O-minimal structures are structures with a dense linear order such that as
few subsets of the line are definable as possible. This condition forces
definable sets in all dimensions to behave in a topologically tame
fashion. But while many properties from semialgebraic geometry carry over
to the o-minimal setting, the question whether one has a theory of
integration in any o-minimal structure is still open. We shall discuss
some partial answers and suggest a possible future direction.
Time and Place
Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47)
Talk at 4:00pm in the KGRC lecture room (seminar room D5.48)
Universität Wien
Institut für Mathematik
Kurt Gödel Research Center
Augasse 2-6, UZA 1 - Building 2
1090 Wien
Logic and Set Theory Seminar: November 5, 3:00 - 3:50 pm
Boise Logic and Set Theory Seminar
11/4/2019
Colleagues,
The next speaker in the Fall 2019 Logic and Set Theory seminar is Dr. Randall Holmes of the Department of Mathematics. Details are as follows:
Location: Mathematics Building Room 124
Date/Time: Tuesday, November 5, 3:00 - 3:50 pm
Title: The Consistency of NFU (and what bearing it has on discourse about paradoxes)
Abstract:I will discuss the typed theory of sets TST, its variant TSTU (actually I tend to think of TST as a variant of TSTU :-) and the consistency proof for R.B. Jensen's variant of Quine's set theory New Foundations.
I will take pains to talk about how the consistency proof with its presentation of a model of NFU (in one of its versions) might help us understand exactly what is going on in the curious ways that NF(U) avoids the paradoxes, the topic of our talk last time.
I shall continue to touch on the theme of mathematical explanation and the basis for our confidence in the reliability of mathematical theories, where appropriate.
Regards,
Marion
Distinguished Professor
Department of Mathematics
Boise State University
Boise, ID 83725
U.S.A.
This Week in Logic at CUNY
This Week in Logic at CUNY
11/3/2019
This Week in Logic at CUNY:
- - - - Monday, Nov 4, 2019 - - - -
Logic and Metaphysics Workshop Date: Monday, November 4, 4.15-6.15 Place: Room 7314, CUNY Graduate Center Speaker: Sergei Artemov (CUNY)
Title: The Provability of Consistency
Abstract: We revisit the foundational question “Can consistency of a theory T be established by means of T?” The usual answer “No, by Gödel’s Second Incompleteness Theorem” is based on two assumptions:
1. Gödel’s internalized consistency formula is the only way to represent consistency. 2. Any contentual reasoning within T internalizes as a formal derivation in T.
We show that already for Peano arithmetic PA both of these assumptions are false: (1) does not cover such legitimate mode of presentation as schemes (think of the Induction scheme), (2) fails for schemes. Based on these observations, we offer a proof of PA-consistency by means of PA and discuss its potential impact.
- - - - Tuesday, Nov 5, 2019 - - - -
Computational Logic Seminar Time 2:00 - 4:00 PM, Room 5382 Tuesday, November 5 Speaker: Sergei Artemov, CUNY Graduate Center Title: On Aggregating Probabilistic Evidence
Abstract: Imagine a database -- a set of propositions S={F_1,F_2,…,F_n} with some kind of probability estimates and let a proposition X logically follow from S. What is the best lower bound of the probability of X? The traditional approach computes a crude numeric lower bound for X from probabilities of F_i's corresponding to a worst-case configuration.
We suggest a more flexible parameterized approach by assuming probability events u_1,u_2,…,u_n which are evidence for F_1,F_2,…,F_n, and calculating “aggregated evidence” e(u_1,u_2,…,u_n) for X. The probability of e provides a tight lower bound for any, not only a worst-case, situation. This model is formalized in Justification Logic and supported by corresponding completeness theorems. With this approach, one can handle conflicting and inconsistent data and gather both positive and negative evidence for the same proposition.
- - - - Wednesday, Nov 6, 2019 - - - -
MOPA (Models of Peano Arithmetic) CUNY Graduate Center, Room 4213.03 (Math Thesis Room) Wednesday, November 6, 6:30-8:00pm Roman Kossak, CUNY Short recursively saturated models of PA as an AEC
Countable short recursively saturated models of PA can serve as bases for abstract elementary classes that are complete but not irreducible. I will explain all these notions and show the construction.
The New York City Category Theory Seminar Department of Computer Science Department of Mathematics The Graduate Center of The City University of New York
Speaker: Dan Shiebler, Oxford. Date and Time: Wednesday November 6, 2019, 7:00 - 8:30 PM., Room 6417. Title: Incremental Monoidal Categories for Speech.
Abstract: In some systems new information is incrementally introduced. For example, each new word in spoken speech modifies the structure and content of a sentence. Although monoidal categories are a popular foundation for linguistic modeling, they are not natively equipped with structure to model incrementality along the tensor-product dimension. In this work we present a characterization of formal grammars as monoidal categories, which we call monoidal grammars. We also characterize automata that parse formal grammars as F-coalgebras. We use these characterizations to derive a functor from the category of monoidal grammars to the category of F-coalgebras.
- - - - Thursday, Nov 7, 2019 - - - -
- - - - Friday, Nov 8, 2019 - - - -
Set Theory Seminar CUNY Graduate Center, Room 6417 Friday, November 8, 10:00-11:45am
Iian Smythe, Rutgers University Parametrized diamonds and mad families of subspaces
In their 2004 paper, Moore, Hrusak and Dzamonja isolated a weakening of Jensen's diamond principle that could be 'parametrized' by a cardinal invariant, implies that the corresponding invariant is small, and yet is consistent with the failure of the Continuum Hypothesis. Moreover, these principles fully determine many cardinal invariants in 'canonical' models, those obtained by iterations of definable proper forcings. I will give a survey of this subject, and then describe a recent application in the study of maximal almost disjoint families of subspaces of a countably infinite-dimensional vector space.
Seminar in Logic, Games and Language Friday, November 8, 2019, 4:15 PM, room 4421 Rohit Parikh, Brooklyn College and CUNY Graduate Center Finite and Infinite Dialogues
We show how "I don't know" can increase someone's knowledge, even into the transfinite. This is a variant of the muddy children but with the games being unbounded.
Next Week in Logic at CUNY:
- - - - Monday, Nov 11, 2019 - - - -
Logic and Metaphysics Workshop Date: Monday, November 11, 4.15-6.15 Place: Room 7314, CUNY Graduate Center
Martin Pleitz (Hamburg) Title: Talking about Reification
Abstract: Reification is the systematic association of a non-object with an object that encodes it. Therefore the reificationist must be a trans-objectist – i.e., anyone who thinks that there are instances of reification must also think that some items are not objects. As exemplified by Frege’s puzzle of the concept horse, non-objects and reification are notoriously difficult to talk about. Therefore I will begin my presentation by outlining a formal language that enables the trans-objectist and the reificationist to speak in a way that is not self-undermining. I will go on and employ the framework to give a uniform diagnosis of the set theoretic and semantic paradoxes in terms of static reification that is an alternative to Graham Priest’s Inclosure Schema, and sketch how dynamic reification can provide a uniform solution to the paradoxes as well as a general account of the constitution of abstract objects. In order to achieve this it will be crucial to import some tools of Procedural Postulationism, a dynamic account of the ontology of mathematics developed by Kit Fine.
- - - - Tuesday, Nov 12, 2019 - - - -
- - - - Wednesday, Nov 13, 2019 - - - -
- - - - Thursday, Nov 14, 2019 - - - -
- - - - Friday, Nov 15, 2019 - - - -
Set Theory Seminar CUNY Graduate Center, Room 6417
Friday, November 15, 10:00-11:45am
Dominik Adolf, Bar-Ilan University Constructing (PCF)-scales through a covering argument
We will present a method of constructing scales on products of regular cardinals. The choice of cardinals depends on the position of 'cutpoints' in the extender sequence of the core model. Here we will only discuss the simplest case of sequences of measures. Scale degrees will correspond to structures occurring in K that will be familiar to some from the construction of square sequences (both global and local) in fine structural inner models. The scale so constructed is canonical, short, and otherwise nice. This work is part of a joint project with Omer Ben-Neria.
Logic Workshop CUNY Graduate Center, Room 6417 Friday, September 15, 2:00-3:30pm
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If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Maciej Malicki, Continuous Logic III
IMPAN Working Group in Applications of Set Theory
11/3/2019
Seminar: Working group in applications of set theory, IMPAN
Thursday, 7.11.2019,
Group lunch (optional): meeting at the reception of IMPAN at 12.30, going to www.wieszcozjesz.pl/1-Danie-dnia (the menu will update)
Seminar at 2:15 pm, room 105, IMPAN, Śniadecki 8, Warsaw.
Speaker: Maciej Malicki (Warsaw School of Economics, SGH)
Title: "Continuous logic III"
Abstact: "This series of talks will be devoted to a gentle introduction to continuous logic - a natural generalization of first-order logic that is suitable in studying mathematical objects equipped with a metric, e.g. Polish metric spaces and groups, Banach spaces, C*-algebras, etc. Continuous logic is surprisingly parallel to classical logic, and all fundamental concepts such as definable sets, algebraic sets, type spaces, quantifier elimination, omitting types, imaginaries, stability, etc., have their counterparts in this setting.
In the third talk, I will continue discussing ultraproducts, and their applications: compactness theorem and a characterization of axiomazatibility. Then I will move to homogeneous, and saturated models.
Literature: Ben Yaacov, Itai; Berenstein, Alexander; Henson, C. Ward; Usvyatsov, Alexander; Model theory for metric structures. Model theory with applications to algebra and analysis. Vol. 2, 315--427, London Math. Soc. Lecture Note Ser., 350, Cambridge Univ. Press, Cambridge, 2008.".
Visit our seminar webpage which may include announcements of some future talks at https://www.impan.pl/~set_theory/Seminar/
Cheers, Piotr.
Wednesday seminar
Prague Set Theory Seminar
10/30/2019
Dear all,
The seminar meets on Wednesday November 6th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Arturo Antonio Martínez Celis Rodríguez -- Rosenthal's lemma
and the reaping number
Rosenthal's lemma is a classical result that concerns sequences of
measures on pairwise disjoint sets and a Rosenthal family is a
collection of infinite subsets of the natural numbers that can replace
the collection of all infinite subsets of natural numbers in Rosenthal's
lemma. In this talk we will study some basic properties of Rosenthal
families and we will see that all ultrafilters are Rosenthal families.
We will also see that the minimal cardinality of a Rosenthal family is
𝔯, where 𝔯 is the reaping/unsplitting number.
Best,
David
Logic Seminar 31 Oct 2019 17:00 hrs at NUS - Change of Speaker
NUS Logic Seminar
10/29/2019
Invitation to the Logic Seminar at the National University of Singapore
Date: Thursday, 31 October 2019, 17:00 hrs
Room: S17#06-11, Department of Mathematics, NUS
Speaker: Marat Arslanov
Title: n-c.e. degrees, CEA operators and fixed-point selection functions.
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: The subjects listed in the title of my talk belong to my steady
scientific interest. In my talk I will speak about my recent work in
these areas and list few open problems that have arisen as a result
of these studies and that I can not answer.
Note: The originally planned talk by Wu Guohua for that day will be moved
to the next semester. Apologies for the short notice change.
UDPATE: This Week in Logic at CUNY
This Week in Logic at CUNY
10/28/2019
Hi everyone,
Please note the addition of Friday's talk by Adam Elga (Princeton University) in the Seminar in Logic, Games and Language.
Best,
Jonas
This Week in Logic at CUNY:
- - - - Monday, Oct 28, 2019 - - - -
Logic and Metaphysics Workshop Date: Tomorrow, Monday, October 28st, 4.15-6.15 Place: Room 7314, CUNY Graduate Center Speaker: Barbara Gail Montero (CUNY) Title: Benacerraf’s Non-Problem
Abstract: Research in philosophy of mathematics over roughly the past half century can be understood, to a large degree, as a series of responses to what is commonly known as the Benacerraf problem: Given the abstract nature of mathematical entities, how can we come to have mathematical knowledge? How are we, in Benacerraf’s words, “to bridge the chasm. . . between the entities that form the subject matter of mathematics and the human knower?” In this talk, I aim to share with you some of the reasons why I think that Benacerraf’s problem—as he presents it and as Field restates it—just may be nothing to worry about.
- - - - Tuesday, Oct 29, 2019 - - - -
Computational Logic Seminar Tuesday, October 29, Time 2:00 - 4:00 PM, Room 5382 Speaker: Hirohiko Kushida, Graduate Center Title: Constructive truth and falsity in Peano Arithmetic
Abstract: Recently, Artemov ( ”The Provability of Consistency”, arXiv preprint arXiv:1902.07404, 2019) pointed out a gap between Hilbert's original program on finitary consistency proof of formal arithmetic and the second incompleteness theorem by Goedel, which has been usually viewed as a negative answer to it. Then, he offered the notion of constructive consistency for Peano Arithmetic and generalized it to constructive truth and falsity in the spirit of Brouwer-Heyting-Kolmogorov semantics and its formalization, the Logic of Proofs.
In this talk, based on these notions, we provide a complete classification of constructive truth and falsity for Friedman's constant fragment of Peano Arithmetic. For this purpose, we generalize the constructive falsity to n-constructive falsity where n is any positive natural number. We also establish similar classification results for constructive truth and n-constructive falsity of Friedman's formulas. Then, we discuss `extremely' independent sentences in the sense that they are classically true but neither constructively true nor n-constructive false for any n.
- - - - Wednesday, Oct 30, 2019 - - - -
MOPA (Models of Peano Arithmetic) CUNY Graduate Center, Room 4213.03 (Math Thesis Room) Wednesday, October 30, 6:30-8:00pm Short recursively saturated models of PA as an AEC
Countable short recursively saturated models of PA can serve as bases for abstract elementary classes that are complete but not irreducible. I will explain all these notions and show the construction.
The New York City Category Theory Seminar Department of Computer Science Department of Mathematics The Graduate Center of The City University of New York Speaker: James Myer. Date and Time: Wednesday October 30, 2019, 7:00 - 8:30 PM., Room 6417. Title: Higher-Order Categorical Logic: Equivalence of Categories. Abstract: We will be starting at Section 0.4 and going forward.
- - - - Thursday, Oct 31, 2019 - - - -
- - - - Friday, Nov 1, 2019 - - - -
Seminar in Logic, Games and Language CUNY Graduate Center, Room 4421 Friday, November 1, 4:15-6:15 Adam Elga (Princeton University) "Causal Decision Theory does not Exist"
Abstract. The box is either empty or contains $1 million (you can't see which). You will either receive (1) just the contents of the box, or (2) the contents of the box plus an extra $1,000. You get to choose (1) or (2). The catch is that a reliable predictor put the $1 million in the box if and only if he predicted you would refuse the extra $1,000. Should you take the $1,000?
This is Newcomb's Problem, which has divided philosophers since it was described by Nozick (1969). Those who favor taking the $1,000 are called "two-boxers" and are typically moved by the sort of "causal dominance reasoning" exemplified by the following speech: "I have no present control over the contents of the box. Whether the box is empty or not, I prefer having an extra $1,000. So I should take the $1,000."
It is often thought that various so-called "causal decision theories" (such as theories described by Stalnaker, Lewis, Gibbard & Harper, Joyce, and others) vindicate causal dominance reasoning, and so are attractive theories for two-boxers. Adapting observations due to Ahmed, Dorr, and Joyce, I argue that those theories do not vindicate causal dominance reasoning in general. Indeed, for each such theory there are Newcomb problems in which the theory recommends *one-boxing*. So none of those theories deserve the name "causal decision theory". I conclude that a true causal decision theory does not exist---or at least, does not exist yet.
Attendees interested in a playful introduction to disputes about Newcomb's problem may optionally wish to look at "Newcomb University: A Play in One Act" <https://philpapers.org/rec/ELGNUA>
(The talk will be self-contained and no advance reading will be presupposed.)
Logic and Metaphysics Workshop Date: Monday, November 4, 4.15-6.15 Place: Room 7314, CUNY Graduate Center Speaker: Sergei Artemov (CUNY)
Title: The Provability of Consistency
Abstract: We revisit the foundational question “Can consistency of a theory T be established by means of T?” The usual answer “No, by Gödel’s Second Incompleteness Theorem” is based on two assumptions:
1. Gödel’s internalized consistency formula is the only way to represent consistency. 2. Any contentual reasoning within T internalizes as a formal derivation in T.
We show that already for Peano arithmetic PA both of these assumptions are false: (1) does not cover such legitimate mode of presentation as schemes (think of the Induction scheme), (2) fails for schemes. Based on these observations, we offer a proof of PA-consistency by means of PA and discuss its potential impact.
- - - - Tuesday, Nov 5, 2019 - - - -
- - - - Wednesday, Nov 6, 2019 - - - -
The New York City Category Theory Seminar Department of Computer Science Department of Mathematics The Graduate Center of The City University of New York
Speaker: Dan Shiebler, Oxford. Date and Time: Wednesday November 6, 2019, 7:00 - 8:30 PM., Room 6417. Title: Incremental Monoidal Categories for Speech.
Abstract: In some systems new information is incrementally introduced. For example, each new word in spoken speech modifies the structure and content of a sentence. Although monoidal categories are a popular foundation for linguistic modeling, they are not natively equipped with structure to model incrementality along the tensor-product dimension. In this work we present a characterization of formal grammars as monoidal categories, which we call monoidal grammars. We also characterize automata that parse formal grammars as F-coalgebras. We use these characterizations to derive a functor from the category of monoidal grammars to the category of F-coalgebras.
- - - - Thursday, Nov 7, 2019 - - - -
- - - - Friday, Nov 8, 2019 - - - -
Set Theory Seminar CUNY Graduate Center, Room 6417 Friday, November 8, 10:00-11:45am
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If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
David Fernández-Bretón: Clases de finitud sin elección
Mexico City Logic Seminar
10/28/2019
Nov. 8, 2019
Instituto de Matemáticas UNAM, Seminarios 3
4:30pm
Existen varias maneras de definir lo que significa que un conjunto sea finito; lo curioso es que, cuando se omite el axioma de elección, no todas estas definiciones son equivalentes. Dada una posible definición de la finitud de un conjunto, a la clase de conjuntos que la satisfacen se le conoce como "clase de finitud", y varios matemáticos han investigado las relaciones que existen entre varias de estas clases. En esta plática, introduciré algunas de estas clases de finitud, con particular énfasis en dos clases en particular que hemos definido hace poco (en colaboración con Joshua Brot y Mengyang Cao) y que se relacionan de manera natural con ciertos teoremas de tipo Ramsey.
Tagged: David Fernández-Bretón
(KGRC) talk in the research seminar October 31
Kurt Godel Research Center
10/28/2019
The KGRC welcomes as guests:
Jana Marikova (host: Benjamin Miller) will stay util June 30, 2020 and
give a talk on November 7.
Clifton Ealy (host: Benjamin Miller) will stay until June 30, 2020.
Sarka Stejskalova (host: Sy-David Friedman) will stay from November 21 to
November 22.
Radek Honzik (host: Sy-David Friedman) will stay from November 21 to
November 22.
Istvan Juhasz (host: Sy-David Friedman) will stay from November 25 to
December 1 and give a talk on November 28.
Miguel Moreno (host: Lyubomyr Zdomskyy) will stay from December 1, 2019 to
November 30, 2020 and give a talk on January 23.
Mohammad Golshani (hosts: Sy-David Friedman, Yair Hayut) will stay from
December 4 to December 11 and give a talk on December 5.
Oleksandr Ravsky (host: Lyubomyr Zdomskyy) will stay from December 9 to
December 22 and give a talk on December 12.
Taras Banakh (host: Lyubomyr Zdomskyy) will stay from December 17, 2019 -
January 3, 2020 and give a talk (talk to be confirmed).
Jaroslav Supina (host: Vera Fischer) will give a talk on January 9, 2020.
Corey Switzer (host: Vera Fischer) will stay from January 12, 2020 to
January 19, 2020 and give a talk on January 16.
Chi Tat Chong (host: Sy-David Friedman) will give a talk on June 18, 2020.
* * *
Research seminar
Kurt Gödel Research Center
Thursday, October 31
"Spectrum of Independence"
Vera Fischer (KGRC)
We will consider some recent results concerning the spectrum of
independence, i.e. the set of cardinalities of maximal independent
families. In particular we will discuss the existence of models in which
the spectrum is finite, models in which the spectrum is countably infinite
and models in which the spectrum is arbitrarily large. If time permits, we
will outline a proof of the consistency of $\mathfrak{i}<\mathfrak{a}_T$,
which brings some light on the long-standing open question of the
consistency of $\mathfrak{i}<\mathfrak{a}$.
Time and Place
Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47)
Talk at 4:00pm in the KGRC lecture room (seminar room D5.48)
Universität Wien
Institut für Mathematik
Kurt Gödel Research Center
Augasse 2-6, UZA 1 - Building 2
1090 Wien
Logic and Set Theory Seminar: October 29, 3:00 - 3:50 pm
Boise Logic and Set Theory Seminar
10/28/2019
Colleagues,
The next speaker in the Fall 2019 Logic and Set Theory seminar is Dr. Randall Holmes of the Department of Mathematics. Details are as follows:
Location: Mathematics Building Room 124
Date/time: Tuesday, October 29, 3:00 - 3:50 pm
Title: The resolution of the paradoxes in NFU
Abstract:I'll present the formal definition of the set theory NFU (New Foundations with urelements) proposed by R.B. Jensen in 1969 as a weakening of Quine's New Foundations (NF) and shown by Jensen to be consistent.
I'll present enough basic implementation of mathematics in NFU to explain why the usual arguments for the paradoxes of Russell, Cantor, and Burali-Forti do not go through in NFU.
The question then presents itself, in the light of the previous talk...in what sense and to what extent can we be taken to be thereby
explaining why we can take NFU to be consistent (or NF, which avoids the paradoxes in the same way, and yet remains dubious)?
The exposition might include a discussion of why we actually do believe that NFU is consistent (Jensen did prove this) and why NF remains doubtful.
Regards,
Marion
Distinguished Professor
Department of Mathematics
Boise State University
Boise, ID 83725
U.S.A.
This Week in Logic at CUNY
This Week in Logic at CUNY
10/27/2019
This Week in Logic at CUNY:
- - - - Monday, Oct 28, 2019 - - - -
Logic and Metaphysics Workshop Date: Tomorrow, Monday, October 28st, 4.15-6.15 Place: Room 7314, CUNY Graduate Center Speaker: Barbara Gail Montero (CUNY) Title: Benacerraf’s Non-Problem
Abstract: Research in philosophy of mathematics over roughly the past half century can be understood, to a large degree, as a series of responses to what is commonly known as the Benacerraf problem: Given the abstract nature of mathematical entities, how can we come to have mathematical knowledge? How are we, in Benacerraf’s words, “to bridge the chasm. . . between the entities that form the subject matter of mathematics and the human knower?” In this talk, I aim to share with you some of the reasons why I think that Benacerraf’s problem—as he presents it and as Field restates it—just may be nothing to worry about.
- - - - Tuesday, Oct 29, 2019 - - - -
Computational Logic Seminar Tuesday, October 29, Time 2:00 - 4:00 PM, Room 5382 Speaker: Hirohiko Kushida, Graduate Center Title: Constructive truth and falsity in Peano Arithmetic
Abstract: Recently, Artemov ( ”The Provability of Consistency”, arXiv preprint arXiv:1902.07404, 2019) pointed out a gap between Hilbert's original program on finitary consistency proof of formal arithmetic and the second incompleteness theorem by Goedel, which has been usually viewed as a negative answer to it. Then, he offered the notion of constructive consistency for Peano Arithmetic and generalized it to constructive truth and falsity in the spirit of Brouwer-Heyting-Kolmogorov semantics and its formalization, the Logic of Proofs.
In this talk, based on these notions, we provide a complete classification of constructive truth and falsity for Friedman's constant fragment of Peano Arithmetic. For this purpose, we generalize the constructive falsity to n-constructive falsity where n is any positive natural number. We also establish similar classification results for constructive truth and n-constructive falsity of Friedman's formulas. Then, we discuss `extremely' independent sentences in the sense that they are classically true but neither constructively true nor n-constructive false for any n.
- - - - Wednesday, Oct 30, 2019 - - - -
MOPA (Models of Peano Arithmetic) CUNY Graduate Center, Room 4213.03 (Math Thesis Room) Wednesday, October 30, 6:30-8:00pm Short recursively saturated models of PA as an AEC
Countable short recursively saturated models of PA can serve as bases for abstract elementary classes that are complete but not irreducible. I will explain all these notions and show the construction.
The New York City Category Theory Seminar Department of Computer Science Department of Mathematics The Graduate Center of The City University of New York Speaker: James Myer. Date and Time: Wednesday October 30, 2019, 7:00 - 8:30 PM., Room 6417. Title: Higher-Order Categorical Logic: Equivalence of Categories. Abstract: We will be starting at Section 0.4 and going forward.
Logic and Metaphysics Workshop Date: Monday, November 4, 4.15-6.15 Place: Room 7314, CUNY Graduate Center Speaker: Sergei Artemov (CUNY)
Title: The Provability of Consistency
Abstract: We revisit the foundational question “Can consistency of a theory T be established by means of T?” The usual answer “No, by Gödel’s Second Incompleteness Theorem” is based on two assumptions:
1. Gödel’s internalized consistency formula is the only way to represent consistency. 2. Any contentual reasoning within T internalizes as a formal derivation in T.
We show that already for Peano arithmetic PA both of these assumptions are false: (1) does not cover such legitimate mode of presentation as schemes (think of the Induction scheme), (2) fails for schemes. Based on these observations, we offer a proof of PA-consistency by means of PA and discuss its potential impact.
- - - - Tuesday, Nov 5, 2019 - - - -
- - - - Wednesday, Nov 6, 2019 - - - -
The New York City Category Theory Seminar Department of Computer Science Department of Mathematics The Graduate Center of The City University of New York
Speaker: Dan Shiebler, Oxford. Date and Time: Wednesday November 6, 2019, 7:00 - 8:30 PM., Room 6417. Title: Incremental Monoidal Categories for Speech.
Abstract: In some systems new information is incrementally introduced. For example, each new word in spoken speech modifies the structure and content of a sentence. Although monoidal categories are a popular foundation for linguistic modeling, they are not natively equipped with structure to model incrementality along the tensor-product dimension. In this work we present a characterization of formal grammars as monoidal categories, which we call monoidal grammars. We also characterize automata that parse formal grammars as F-coalgebras. We use these characterizations to derive a functor from the category of monoidal grammars to the category of F-coalgebras.
- - - - Thursday, Nov 7, 2019 - - - -
- - - - Friday, Nov 8, 2019 - - - -
Set Theory Seminar CUNY Graduate Center, Room 6417 Friday, November 8, 10:00-11:45am
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Wednesday seminar
Prague Set Theory Seminar
10/27/2019
Dear all,
The seminar meets on Wednesday October 30th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Noé de Rancourt -- A local Ramsey theorem for P+ coindeals.
Abstract: I will prove a local Ramsey theorem for P+ co-ideals which is
the direct generalization of Mathias' theorem for selective co-ideals.
Best,
David
Logic Seminar 31 Oct 2019 17:00 hrs at NUS
NUS Logic Seminar
10/25/2019
Invitation to the Logic Seminar at the National University of Singapore
Date: Thursday, 31 October 2019, 17:00 hrs
Room: S17#06-11, Department of Mathematics, NUS
Speaker: Wu Guohua
Title: Lachlan degrees: their distribution and applications
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: Lachlan observed that d.r.e. degrees are downwards dense, by
using a nonuniform argument, where the so-called Lachlan sets were
proposed. Shamil started to consider the possible (r.e.) degrees of
Lachlan sets, and showed that for various d.r.e. degrees, the
corresponding Lachlan degree could be singletons, or intervals. Shamil
even constructed d.r.e. degrees such that the associated Lachlan degrees
do not have minimium. In this talk, I will briefly review our work in this
direction, including our recent work on nonbounding phenomenon.
(KGRC) talk in the research seminar October 24
Kurt Godel Research Center
10/21/2019
The KGRC welcomes as guests:
Jana Marikova (host: Benjamin Miller) will stay util June 30, 2020
and give a talk on November 7.
Clifton Ealy (host: Benjamin Miller) will stay until June 30, 2020.
Yurii Khomskii (host: Vera Fischer) will stay until October 27 and give a
talk on October 24 (see below).
István Juház (host: Sy-David Friedman) will stay from November 25 to
December 1 and give a talk on November 28.
Miguel Moreno (host: Lyubomyr Zdomskyy) will stay from December 1, 2019 to
November 30, 2020 and give a talk on January 23.
Mohammad Golshani (hosts: Sy-David Friedman, Yair Hayut) will stay from
December 4 to December 11 and give a talk on December 5.
Oleksandr Ravsky (host: Lyubomyr Zdomskyy) will stay from December 9
to December 22 and give a talk on December 12.
Taras Banakh (host: Lyubomyr Zdomskyy) will stay from December 16,
2019 - January 3, 2020 and give a talk on December 17.
Jaroslav Supina (host: Vera Fischer) will give a talk on January 9, 2020.
Corey Switzer (host: Vera Fischer) will stay from January 12, 2020 to
January 19, 2020 and give a talk on January 16.
Chi Tat Chong (host: Sy-David Friedman) will give a talk on June 18,
2020.
* * *
Research seminar
Kurt Gödel Research Center
Thursday, October 24
"Symbiosis and Upwards Reflection"
Yurii Khomskii
(Amsterdam University College, Netherlands and Hamburg University,
Germany)
In [1], Bagaria and Väänänen developed a framework for studying the large
cardinal strength of Löwenheim-Skolem theorems of strong logics using the
notion of Symbiosis (originally introduced by Väänänen in his PhD Thesis).
Symbiosis provides a way of relating model theoretic properties of strong
logics to definability in set theory. We continue the systematic
investigation of Symbiosis and apply it to upwards Löwenheim-Skolem
theorems (and partially to compactness properties). As an application, we
provide some upper and lower bounds of the large cardinal strength of
upwards Löwenheim-Skolem-type theorems of second order logic.
This is joint work with Lorenzo Galeotti and Jouko Väänänen.
[1] Joan Bagaria and Jouko Väänänen, "On the Symbiosis Between
Model-Theoretic and Set-Theoretic Properties of Large Cardinals", Journal
of Symbolic Logic 81 (2) P. 584-604
Time and Place
Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47)
Talk at 4:00pm in the KGRC lecture room (seminar room D5.48)
Universität Wien
Institut für Mathematik
Kurt Gödel Research Center
Augasse 2-6, UZA 1 - Building 2
1090 Wien
(KGRC) Correction: talk in the research seminar October 24
Kurt Godel Research Center
10/21/2019
The announcement a few minutes ago failed to include time and place
for the talk. Apologies for this mistake! Here is the complete
announcement:
The KGRC welcomes as guests:
Jana Marikova (host: Benjamin Miller) will stay util June 30, 2020 and
give a talk on November 7.
Clifton Ealy (host: Benjamin Miller) will stay until June 30, 2020.
Yurii Khomskii (host: Vera Fischer) will stay until October 27 and give a
talk on October 24 (see below).
István Juház (host: Sy-David Friedman) will stay from November 25 to
December 1 and give a talk on November 28.
Miguel Moreno (host: Lyubomyr Zdomskyy) will stay from December 1, 2019 to
November 30, 2020 and give a talk on January 23.
Mohammad Golshani (hosts: Sy-David Friedman, Yair Hayut) will stay from
December 4 to December 11 and give a talk on December 5.
Oleksandr Ravsky (host: Lyubomyr Zdomskyy) will stay from December 9 to
December 22 and give a talk on December 12.
Taras Banakh (host: Lyubomyr Zdomskyy) will stay from December 16, 2019 -
January 3, 2020 and give a talk on December 17.
Jaroslav Supina (host: Vera Fischer) will give a talk on January 9, 2020.
Corey Switzer (host: Vera Fischer) will stay from January 12, 2020 to
January 19, 2020 and give a talk on January 16.
Chi Tat Chong (host: Sy-David Friedman) will give a talk on June 18, 2020.
* * *
Research seminar
Kurt Gödel Research Center
Thursday, October 24
"Symbiosis and Upwards Reflection"
Yurii Khomskii
(Amsterdam University College, Netherlands and Hamburg University, Germany)
In [1], Bagaria and Väänänen developed a framework for studying the large
cardinal strength of Löwenheim-Skolem theorems of strong logics using the
notion of Symbiosis (originally introduced by Väänänen in his PhD Thesis).
Symbiosis provides a way of relating model theoretic properties of strong
logics to definability in set theory. We continue the systematic
investigation of Symbiosis and apply it to upwards Löwenheim-Skolem
theorems (and partially to compactness properties). As an application, we
provide some upper and lower bounds of the large cardinal strength of
upwards Löwenheim-Skolem-type theorems of second order logic.
This is joint work with Lorenzo Galeotti and Jouko Väänänen.
[1] Joan Bagaria and Jouko Väänänen, "On the Symbiosis Between
Model-Theoretic and Set-Theoretic Properties of Large Cardinals", Journal
of Symbolic Logic 81 (2) P. 584-604
Time and Place
Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47)
Talk at 4:00pm in the KGRC lecture room (seminar room D5.48)
Universität Wien
Institut für Mathematik
Kurt Gödel Research Center
Augasse 2-6, UZA 1 - Building 2
1090 Wien
(KGRC) talk in the research seminar October 24
Kurt Godel Research Center
10/21/2019
The KGRC welcomes as guests:
Jana Marikova (host: Benjamin Miller) will stay util June 30, 2020
and give a talk on November 7.
Clifton Ealy (host: Benjamin Miller) will stay until June 30, 2020.
Yurii Khomskii (host: Vera Fischer) will stay until October 27 and give a
talk on October 24 (see below).
István Juház (host: Sy-David Friedman) will stay from November 25 to
December 1 and give a talk on November 28.
Miguel Moreno (host: Lyubomyr Zdomskyy) will stay from December 1, 2019 to
November 30, 2020 and give a talk on January 23.
Mohammad Golshani (hosts: Sy-David Friedman, Yair Hayut) will stay from
December 4 to December 11 and give a talk on December 5.
Oleksandr Ravsky (host: Lyubomyr Zdomskyy) will stay from December 9
to December 22 and give a talk on December 12.
Taras Banakh (host: Lyubomyr Zdomskyy) will stay from December 16,
2019 - January 3, 2020 and give a talk on December 17.
Jaroslav Supina (host: Vera Fischer) will give a talk on January 9, 2020.
Corey Switzer (host: Vera Fischer) will stay from January 12, 2020 to
January 19, 2020 and give a talk on January 16.
Chi Tat Chong (host: Sy-David Friedman) will give a talk on June 18,
2020.
* * *
Research seminar
Kurt Gödel Research Center
Thursday, October 24
"Symbiosis and Upwards Reflection"
Yurii Khomskii
(Amsterdam University College, Netherlands and Hamburg University,
Germany)
In [1], Bagaria and Väänänen developed a framework for studying the large
cardinal strength of Löwenheim-Skolem theorems of strong logics using the
notion of Symbiosis (originally introduced by Väänänen in his PhD Thesis).
Symbiosis provides a way of relating model theoretic properties of strong
logics to definability in set theory. We continue the systematic
investigation of Symbiosis and apply it to upwards Löwenheim-Skolem
theorems (and partially to compactness properties). As an application, we
provide some upper and lower bounds of the large cardinal strength of
upwards Löwenheim-Skolem-type theorems of second order logic.
This is joint work with Lorenzo Galeotti and Jouko Väänänen.
[1] Joan Bagaria and Jouko Väänänen, "On the Symbiosis Between
Model-Theoretic and Set-Theoretic Properties of Large Cardinals", Journal
of Symbolic Logic 81 (2) P. 584-604
Time and Place
Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47)
Talk at 4:00pm in the KGRC lecture room (seminar room D5.48)
Universität Wien
Institut für Mathematik
Kurt Gödel Research Center
Augasse 2-6, UZA 1 - Building 2
1090 Wien
Logic and Set Theory Seminar: October 22, 3:00 - 3:50 pm
Boise Logic and Set Theory Seminar
10/21/2019
Colleagues,
The next speaker in the Fall 2019 Logic and Set Theory seminar is Dr. Edward Ferrier of the Philosophy Department. Details are as follows:
Location: Mathematics Building Room 124
Date/time: Tuesday, October 22, 3:00 - 3:50 pm
Title: Explanation and Paradox
Abstract:Recently, there has been much interest in mathematical explanation. While there is no general account of precisely what this consists in, it is generally agreed that some mathematical proofs are more explanatory than others. I will discuss the explanatory virtues of proofs that contradiction-inducing sets, such as the universal set, do not exist in standard ZFC set theory. Do these proofs explain why these sets don't exist? Do they help explain the consistency of ZFC? Finally, do the explanations we seek rely on the so-called ``iterative conception of set''? And what sorts of pressures do our explanatory demands place on this conception?
Regards,
Marion
Distinguished Professor
Department of Mathematics
Boise State University
Boise, ID 83725
U.S.A.
This Week in Logic at CUNY
This Week in Logic at CUNY
10/20/2019
This Week in Logic at CUNY:
- - - - Monday, Oct 21, 2019 - - - -
Logic and Metaphysics Workshop Date: Tomorrow, Monday, October 21st, 4.15-6.15 Place: Room 7314, CUNY Graduate Center Speaker: Rohit Parikh (CUNY) Title: The Buddha versus Popper: When to Live?
Abstract: We discuss two approaches to life: presentism and futurism. The first one, which we are identifying with the Buddha, is to live in the present and not to allow the future to hinder us from living in the ever present now. The second one, which we will identify with Karl Popper, is to think before we act, and act now for a better future. We will discuss various aspects of presentism and futurism, such as Ruth Millikan’s Popperian animal, the psychologist Howard Rachlin’s social and temporal discounting, and even the popular but controversial idea, YOLO (you live only once). The purpose of this talk is to contrast one with the other. The central question of ethics is: How should one live? Our variation on that question is: When should one live? We conjecture that the notion of flow, developed by Csikszentmihalyi, may be a better optimal choice between these two positions. [Note: This work, which is joint with Jongjin Kim, is to appear in the Journal of Buddhist Ethics.]
- - - - Tuesday, Oct 22, 2019 - - - -
Computational Logic Seminar Fall Semester 2019 Tuesday, October 22, Time 2:00 - 4:00 PM, Room 5382 Speaker: Vincent Peluce, CUNY Graduate Center Title: The Perception of Time in Intuitionistic Arithmetic
Abstract: L.E.J. Brouwer famously took the subject’s intuition of time to be foundational and from there ventured to build up mathematics. For reasons in Brouwerian philosophy, properly intuitionistic mathematics cannot be not tied to any particular formal system. Despite this, we know that he still saw value in axiomatic systems for their use in communication and memory. Through the Dutch Mathematical Society, Gerrit Mannoury posed the challenge to provide an axiomatization of intuitionistic arithmetic. Arend Heyting’s axiomatization was chosen as the winner and has since enjoyed the status as accepted solution to Mannoury’s challenge. We argue that axiomatizations of intuitionistic arithmetic (and reasoning more generally) ought to make explicit the subject. Though Heyting Arithmetic provides an important base for intuitionistic arithmetic in characterizing the subject’s perception of time, it leaves out the subject, and thus, we suggest, falls short as a response to Mannoury’ challenge. We offer our own solution, Doxastic Heyting Arithmetic, or DHA, which we contend adequately axiomatizes Brouwerian intuitionistic arithmetic.
- - - - Wednesday, Oct 23, 2019 - - - -
The New York City Category Theory Seminar Department of Computer Science Department of Mathematics The Graduate Center of The City University of New York Speaker: Alex Martsinkovsky, Northeastern University.
Date and Time: Wednesday October 23, 2019, 7:00 - 8:30 PM., Room 6417. Title: Stabilization of additive functors II.
Abstract: Over the last couple of years we have seen a growing number of unexpected applications of stabilized functors. This term refers to the passage from an additive functor between abelian categories to a functor vanishing on injectives (or projectives). This concept has been around since M. Auslander’s pioneering work in the mid-1960s, but apparently not much work has been done on it later on. In my previous talk (December 2018) I gave precise definitions and outlined two applications: an extension of the Auslander-Reiten formula and a generalization of Tate homology, both applicable to arbitrary modules over arbitrary rings.
In the present talk, I will review the definitions and will present yet another application of stabilization. First, we shall redefine and extend the classical torsion over commutative domains. This algebraic concept goes back to Poincaré, who described (and named) it in a topological setting around 1900. In 1959, Bass observed that the kernel of the canonical bidualization map, which we call the Bass torsion, from a finitely generated module over a commutative domain coincides with the classical torsion of the module. Using the injective stabilization of the tensor product, Jeremy Russell and I defined, for arbitrary modules over arbitrary rings, a new torsion radical, which agrees with both the classical torsion over commutative domains and the Bass torsion for finitely presented modules over arbitrary rings. The functorial nature of the new torsion makes it amenable to dualization, yielding, for the first time, a notion of cotorsion, also applicable to arbitrary modules over arbitrary rings. The informal, metamathematical dualization process used to define the cotorsion can be effected by a purely mathematical tool, known as the Auslander-Gruson-Jensen functor.
- - - - Thursday, Oct 24, 2019 - - - -
- - - - Friday, Oct 25, 2019 - - - -
Model Theory Seminar CUNY Graduate Center, Room 6417 Friday, October 25, 12:30-2:00pm Alice Medvedev, CUNY TBA
Logic Workshop CUNY Graduate Center, Room 6417 Friday, October 25, 2:00-3:30pm
Jouko Väänänen, University of Helsinki On an extension of a theorem of Zermelo
Zermelo (1930) proved the following categoricity result for set theory: Suppose M is a set and E, E’ are two binary relations on M. If both (M, E) and (M, E’) satisfy the second order Zermelo–Fraenkel axioms, then (M,E) and (M, E’) are isomorphic. Of course, the same is not true for first order ZFC. However, we show that if first order ZFC is formulated in the extended vocabulary {E,E’}, then Zermelo’s result holds even in the first order case. Similarly, Dedekind’s categoricity result (1888) for second order Peano arithmetic has an extension to a result about first order Peano.
Next Week in Logic at CUNY:
- - - - Monday, Oct 28, 2019 - - - -
Logic and Metaphysics Workshop Date: Tomorrow, Monday, October 28st, 4.15-6.15 Place: Room 7314, CUNY Graduate Center Speaker: Barbara Gail Montero (CUNY) Title: Benacerraf’s Non-Problem
Abstract: Research in philosophy of mathematics over roughly the past half century can be understood, to a large degree, as a series of responses to what is commonly known as the Benacerraf problem: Given the abstract nature of mathematical entities, how can we come to have mathematical knowledge? How are we, in Benacerraf’s words, “to bridge the chasm. . . between the entities that form the subject matter of mathematics and the human knower?” In this talk, I aim to share with you some of the reasons why I think that Benacerraf’s problem—as he presents it and as Field restates it—just may be nothing to worry about.
- - - - Tuesday, Oct 29, 2019 - - - -
- - - - Wednesday, Oct 30, 2019 - - - -
The New York City Category Theory Seminar Department of Computer Science Department of Mathematics The Graduate Center of The City University of New York Speaker: James Myer. Date and Time: Wednesday October 30, 2019, 7:00 - 8:30 PM., Room 6417. Title: Higher-Order Categorical Logic: Equivalence of Categories. Abstract: We will be starting at Section 0.4 and going forward.
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If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Wednesday seminar
Prague Set Theory Seminar
10/18/2019
Dear all,
The seminar meets on Wednesday October 23rd at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
There is no fixed program yet, walk-in speakers will be welcome. The
backup topic is me talking (overview) about destroying tallness of
ideals on omega with forcing.
Best,
David
Logic Seminar 24 Oct 2019 17:00 hrs at NUS
NUS Logic Seminar
10/18/2019
Invitation to the Logic Seminar at the National University of Singapore
Date: Thursday, 24 October 2019, 17:00 hrs
Room: S17#06-11, Department of Mathematics, NUS
Speaker: Yang Yue
Title: Ramsey's Theorem on trees and weak Koenig's Lemma
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Ramsey's Theorem for Pairs has been studied intensively in reverse
mathematics. One of the major breakthroughs is Liu Lu's 2012 result
showing RT-2-2 does not imply WKL-0.
Liu's result not only answered an important question in reverse
mathematics, the technique that he used turns out to have wider applications,
for example, in Monin and Patey's separation of SRT-2-2 and RT-2-2.
In this talk, we generalize Liu's result to tree. Let TT-2-k denote
the combinatorial principle stating that every k-coloring of pairs
of compatible nodes on the full binary tree has a homogeneous
solution, i.e. an infinite perfect tree in which all pairs of
compatible nodes have the same color. We show that over the base
system RCA-0, TT-2-k doe not imply weak Koenig's lemma.
This is joint work with Chong Chitat, Li Wei and Liu Lu.
This Week in Logic at CUNY
This Week in Logic at CUNY
10/14/2019
This Week in Logic at CUNY:
- - - - Monday, Oct 14, 2019 - - - -
- - - - Tuesday, Oct 15, 2019 - - - -
- - - - Wednesday, Oct 16, 2019 - - - -
MOPA (Models of Peano Arithmetic) CUNY Graduate Center, Room 4213.03 (Math Thesis Room) Wednesday, October 16, 6:30-8:00pm
Alf Dolich, CUNY Getting Atomic Models of Size Continuum
Following Baldwin and Laskowski's 'Henkin Constructions of Models of Size Continuum' I will outline how the main results of this paper can be used to show that under a variety of assumptions a theory T with an uncountable atomic model also has an atomic model of size continuum.
- - - - Thursday, Oct 17, 2019 - - - -
- - - - Friday, Oct 18, 2019 - - - -
Model Theory Seminar CUNY Graduate Center, Room 6417 Friday, October 18, 12:30-2:00pm
Russell Miller, CUNY Model Completeness and Relative Decidability
Model-completeness is a standard notion in model theory, and it is well known that a theory TT is model complete if and only if TT has quantifier elimination down to existential formulas. From the quantifier elimination, one quickly sees that every computable model of a computably enumerable, model-complete theory TT must be decidable. We call a structure relatively decidable if this holds more broadly: if for all its copies AA with domain ωω, the elementary diagram of AA is Turing-reducible to the atomic diagram of AA. In some cases, this reduction can be done uniformly by a single Turing functional for all copies of AA, or even for all models of a theory TT.
We discuss connections between these notions. For a c.e. theory, model completeness is equivalent to uniform relative decidability of all countable models of the theory, but this fails if the condition of uniformity is excluded. On the other hand, for relatively decidable structures where the reduction is not uniform, it can be made uniform by expanding the language by finitely many constants to name certain specific elements. This is shown by a priority construction related to forcing. We had conjectured that a similar result might hold for theories TT such that every model of TT is relatively decidable, but in separate work, Matthew Harrison-Trainor has now shown relative decidability to be a Π11Π11-complete property of a theory, which is far more complicated than our conjectured equivalent property.
This is joint work with Jennifer Chubb and Reed Solomon.
Logic Workshop CUNY Graduate Center, Room 6417 Friday, October 18, 2:00-3:30pm
Philipp Rothmaler, CUNY
High and low formulas in the model theory of modules
A positive primitive (henceforth pp) formula is an existentially quantified (i.e., a projection of a) finite system of linear equations (over a given associative ring R). In this talk I am interested exclusively in such formulas with one free variable. I call such a formula high if, in every injective module E, it defines all of E. Note, the high formulas form a filter in the lattice of all unary pp formulas. Long time ago I discovered this dichotomy: every (unary) pp formula is either high or else bounded (but not both), which means that there is a nonzero ring element that annihilates, in every module, all of the set defined by the formula (which is, in fact, an additive subgroup of the module).
I had not given this much further thought until recently, when I discovered, in collaboration with A. Martsinkovsky, that the dual notion of low formula gives rise to a torsion theory, namely injective torsion as introduce by him and J. Russell in recent work. I call a formula low if it vanishes on the flat modules, or, equivalently, on the ring as a module over itself. Note, the low formulas form an ideal in the lattice of all unary pp formulas. I will explain how elementary duality (as introduced by Prest and Herzog) yields at once another dichotomy: every pp formula is either low or else cobounded (but not both), where this means, dually, that the action of some nonzero ring element sends every module into the subgroup defined by that formula.
Interestingly, these two dichotomies are, in general, completely independent. But I will show how their interplay can be used to characterize (not necessarily commutative) domains within the class of all rings, and one-sided Ore domains and also two-sided Ore domains within all domains. (Commutative domains are two-sided Ore.)
Seminar in Logic, Games and Language CUNY Graduate Center, Room 4421 Friday, October 18, 4:15-6:15 Arthur Paul Pedersen, CUNY Brooklyn College "Bayesian Aggregation under Severe Uncertainty and Unresolved Conflict"
Abstract. I'll examine the problem of aggregating judgments of a group of individuals. What criteria are to serve as normative standards for reaching Bayesian consensus? This talk has two parts. As background, for the first of this talk I'll discuss (i) external vs internal Bayesianism (update then aggregate vs. aggregate then update) and (ii) Bayesian extensions of Arrow-like impossibility theorems and their counterpart possibility theorems. Do the purported normative standards extend to conditions of severe uncertainty or unresolved conflict? Do normative standards appropriate to common conditions such as these avoid Arrow-like impossibility theorems?
For the second part of this talk, I'll turn to (iii) incompleteness vs. indeterminacy in probability and utility judgment (tentative vs. assertive incompleteness), (iv) set-valued judgment aggregation under conditions of contradictory or incomplete information or unresolved conflict, (v) the problem of dilation, and (vi) the return of Arrow-like impossibility theorems, as well as some possibility theorems.
NOTE: On Friday, October 25, the Seminar in Logic, Games and Language will not meet at CUNY but will be replaced by a talk at Columbia University in the seminar in logic, probability and games.
Next Week in Logic at CUNY:
- - - - Monday, Oct 21, 2019 - - - -
- - - - Tuesday, Oct 22, 2019 - - - -
- - - - Wednesday, Oct 23, 2019 - - - -
- - - - Thursday, Oct 24, 2019 - - - -
- - - - Friday, Oct 25, 2019 - - - -
Logic Workshop CUNY Graduate Center, Room 6417 Friday, October 25, 2:00-3:30pm
Jouko Väänänen, University of Helsinki On an extension of a theorem of Zermelo
Zermelo (1930) proved the following categoricity result for set theory: Suppose M is a set and E, E’ are two binary relations on M. If both (M, E) and (M, E’) satisfy the second order Zermelo–Fraenkel axioms, then (M,E) and (M, E’) are isomorphic. Of course, the same is not true for first order ZFC. However, we show that if first order ZFC is formulated in the extended vocabulary {E,E’}, then Zermelo’s result holds even in the first order case. Similarly, Dedekind’s categoricity result (1888) for second order Peano arithmetic has an extension to a result about first order Peano.
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Logic and Set Theory Seminar: October 15, 3:00 - 3:50 pm
Boise Logic and Set Theory Seminar
10/14/2019
Colleagues,
The next speaker in the Fall 2019 Logic and Set Theory seminar is Dr. Sam Coskey of the Department of Mathematics. Details are as follows:
Location: Mathematics Building Room 124
Date/time: Tuesday, October 15, 3:00 - 3:50 pm
Title: On conjugacy problems for graphs and trees
Abstract:Given a graph or tree G, the conjugacy problem for G is the conjugacy equivalence relation on the group Aut(G) of automorphisms of G. In this talk we will introduce the basic framework for studying the complexity of the conjugacy problem for G, and then use it to examine a series of examples of graphs and trees G. In particular we will demonstrate that a variety of complexities can occur, from trivial (smooth), up to maximally complex (Borel complete), and in between.
Regards,
Marion
Distinguished Professor
Department of Mathematics
Boise State University
Boise, ID 83725
U.S.A.
Logic Seminar 17 Oct 2019 17:00 hrs at NUS
NUS Logic Seminar
10/14/2019
Invitation to the Logic Seminar at the National University of Singapore
Date: Thursday, 17 October 2019, 17:00 hrs
Room: S17#06-11, Department of Mathematics, NUS
Speaker: Li Zeyong
Title: A Complete Problem for Statistical Zero Knowledge
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
This work by Amit Sahai and Salil Vadhan presents the first complete
problem for SZK, the class of promise problems possessing statistical
zero-knowledge proofs (against an honest verifier). The problem, called
STATISTICAL DIFFERENCE, is to decide whether two efficiently samplable
distributions are either statistically close or far apart. This gives a
new characterization of SZK that makes no reference to interaction or zero
knowledge.
The talk (due to time constraint) will focus on the second half (and
arguably the more insightful half) of the completeness theorem, that is,
STATISTICAL DIFFERENCE is SZK-hard. It essentially gives a constructive
proof that any promise problem possessing a statistical zero-knowledge
proof can be reduced to an instance of STATISTICAL DIFFERENCE in
polynomial time.
The paper of Sahai and Vadhan is available from Sahai's webpage at
http://web.cs.ucla.edu/~sahai/work/web/2003%20Publications/J.ACM2003.pdf
Menachem Kojman: Strong Colorings
Catania Set Theory and Topology Seminar
10/14/2019
Title: Strong Colorings
Speaker: Menachem Kojman, Ben Gurion University, Israel
Date and time: Thursday, October 17, 2019, 4 PM.
Room: Aula Anile, Department of Mathematics and Computer Science, University of Catania, Italy
Abstract: A strong $\mu$-coloring on a cardinal $\kappa$ is a function $f:[\kappa]^2\to \mu$ --- a coloring of unordered pairs from $\kappa$ with $\mu$ colors --- with the property that for every $A\subseteq \k$ of cardinality $\kappa$, all $\mu$ colors occur on $[A]^2$, that is, for every $\gamma<\kappa$ there are $\alpha<\beta$ in $A$ such that $f(\{\a,\b\})=\gamma$.
Sierpinski constructed a $2$-strong coloring on $\aleph_1$ and later strong colorings with various additional properties were constructed by Erd\H os and H\'ajnal with the GCH. Todorcevic introduced the method of "minimal walks" or "ordinal walks" and with it constructed a strong $\aleph_1$ coloring on $\aleph_1$.
We shall present a short proof of Todorcevic's coloring and discuss stronger versions of strong colorings, in particular the one defined by Shelah, following Galvin, which enables the construction of two topological spaces each of which satisfies the $\kappa^+$-chain conditions but whose product fails it.
Tagged: Menachem Kojman
Maciej Malicki, Continuous Logic II
IMPAN Working Group in Applications of Set Theory
10/13/2019
Seminar: Working group in applications of set theory, IMPAN
Thursday, 17.10.2019,
Group lunch (optional): meeting at the reception of IMPAN at 12.30, going to www.wieszcozjesz.pl/1-Danie-dnia (the menu will update)
Seminar at 2:15 pm, room 105, IMPAN, Śniadecki 8, Warsaw.
Speaker: Maciej Malicki (Warsaw School of Economics, SGH)
Title: "Continuous logic"
Abstact: "This series of talks will be devoted to a gentle introduction to continuous logic - a natural generalization of first-order logic that is suitable in studying mathematical objects equipped with a metric, e.g. Polish metric spaces and groups, Banach spaces, C*-algebras, etc. Continuous logic is surprisingly parallel to classical logic, and all fundamental concepts such as definable sets, algebraic sets, type spaces, quantifier elimination, omitting types, imaginaries, stability, etc., have their counterparts in this setting.
In the second talk, I will discuss full sets of connectives, ultraproducts, and their applications: compactness theorem and axiomazatibility. If time pertmits, I will also prove the downward Lowenheim- Skolem theorem, and say something about saturated models.
Literature: Ben Yaacov, Itai; Berenstein, Alexander; Henson, C. Ward; Usvyatsov, Alexander; Model theory for metric structures. Model theory with applications to algebra and analysis. Vol. 2, 315--427, London Math. Soc. Lecture Note Ser., 350, Cambridge Univ. Press, Cambridge, 2008.".
Visit our seminar webpage which may include announcements of some future talks at https://www.impan.pl/~set_theory/Seminar/
Cheers, Piotr.
Wednesday seminar
Prague Set Theory Seminar
10/11/2019
Dear all,
There is no seminar next week (October 16).
The seminar will meet again on Wednesday October 23rd.
Best,
David
(KGRC) talk in the research seminar October 17
Kurt Godel Research Center
10/10/2019
The KGRC welcomes Jana Marikova, Clifton Ealy, Alexander Osipov, Christina
Brech, Michal Tomasz Godziszewski, Istvan Juhaz, Miguel Moreno, Mohammad
Golshani, Oleksandr Ravsky, Taras Banakh, Jaroslav Supina, Corey Switzer
and Chi Tat Chong as guests.
Professor Marikova (host: Benjamin Miller) will stay util June 30, 2020.
Professor Ealy (host: Benjamin Miller) will stay until June 30, 2020. Dr.
Osipov (host: Lyubomyr Zdomskyy) will stay until Oktober 12. Professor
Brech (host: Lyubomyr Zdomskyy) will stay until October 12. Mr.
Godziszewski (host: Vera Fischer) will give a talk on October 17 (see
below). Dr. Moreno (host: Lyubomyr Zdomskyy) will stay from December 1,
2019 to November 30, 2020. Dr. Golshani (hosts: Sy-David Friedman, Yair
Hayut) will stay from December 4 to December 11 and give a talk on
December 5. Dr. Ravsky (host: Lyubomyr Zdomskyy) will stay from December 9
to December 22. Professor Banakh (host: Lyubomyr Zdomskyy) will stay from
December 16, 2019 - January 3, 2020. Dr. Supina (host: Vera Fischer) will
give a talk on January 9, 2020. Mr. Switzer (host: Vera Fischer) will stay
from January 12, 2020 to January 19, 2020 and give a talk on January 16.
Professor Chong (host: Sy-David Friedman) will give a talk on June 18,
2020.
* * *
Research seminar
Kurt Gödel Research Center
Thursday, October 17
"The Multiverse, Recursive Saturation and Well-Foundedness Mirage"
Michal Tomasz Godziszewski
(Munich Center for Mathematical Philosophy, Universität München,
Germany)
Recursive saturation, introduced by J. Barwise and J. Schlipf is a robust
notion which has proved to be important for the study of nonstandard
models (in particular, it is ubiquitous in the model theory of axiomatic
theories of truth, e.g. in the topic of satisfaction classes, where one
can show that if $M \models ZFC$ is a countable $\omega$-nonstandard
model, then $M$ admits a satisfaction class iff $M$ is recursively
saturated). V. Gitman and J. Hamkins showed in \emph{A Natural Model of
the Multiverse Axioms} that the collection of countable, recursively
saturated models of set theory satisfy the so-called Hamkins's Multiverse
Axioms. The property that forces all the models in the Multiverse to be
recursively saturated is the so-called Well-Foundedness Mirage axiom which
asserts that every universe is $\omega$-nonstandard from the perspective
of some larger universe, or to be more precise, that: if a model $M$ is in
the multiverse then there is a model $N$ in the multiverse such that $M$
is a set in $N$ and $N \models 'M \text{ is }
$\omega$-\text{nonstandard.'}$. Inspection of the proof led to a question
if the recursive saturation could be avoided in the Multiverse by
weakening the Well-Foundedness Mirage axiom. Our main results answer this
in the positive. We give two different versions of the Well-Foundedness
Mirage axiom -- what we call Weak Well-Foundedness Mirage (saying that if
$M$ is a model in the Multiverse then there is a model $N$ in the
Multiverse such that $M \in N$ and $N \models 'M \text{ is
nonstandard.'}$.) and Covering Well-Foundedness Mirage (saying that if $M$
is a model in the Multiverse then there is a model $N$ in the Multiverse
with $K \in N$ such that $K$ is an end-extension of $M$ and $N \models 'K
\text{ is } $\omega$-\text{nonstandard.'}$). I will present constructions
of two different Multiverses satisfying these two weakened axioms.
This is joint work with V. Gitman. T. Meadows and K. Williams.
Time and Place
Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47)
Talk at 4:00pm in the KGRC lecture room (seminar room D5.48)
Universität Wien
Institut für Mathematik
Kurt Gödel Research Center
Augasse 2-6, UZA 1 - Building 2
1090 Wien
Invitation to the Logic Seminar at the National University of Singapore
Date: Thursday, 10 October 2019, 17:00 hrs
Room: S17#06-11, Department of Mathematics, NUS
Speaker: Ashutosh Kumar
Title: On partitions into null sets
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Given a partition P of the set of reals into Lebesgue null sets,
let J be the ideal of those subsets of P whose union is null. We'll
show that, consistently, J can be countably saturated.
This is a joint work with Saharon Shelah.
Alfonso Ruiz: Clasificación de las teorías matemáticas (según Shelah)
Mexico City Logic Seminar
10/8/2019
Oct. 18, 2019
Instituto de Matemáticas UNAM, Seminarios 3
4:30pm
Por medio de ejemplos y de cualidades importantes sobre las teorías (clases elementarias y combinatoria) hablaremos de una clasificación de las teorías matemáticas que comienza en dificultad con espacios vectoriales de dimensión finita y termina con la aritmética (teorema de incompletud de Gödel). Hrushovski y su escuela han distinguido entre las teorías intermedias a las mejores herramientas para aplicar la lógica matemática a otras áreas de las matemáticas.
Tagged: Alfonso Ruiz
This Week in Logic at CUNY
10/6/2019
This Week in Logic at CUNY:
- - - - Monday, Oct 7, 2019 - - - -
Logic and Metaphysics Workshop Date: Tomorrow, Monday, October 7th, 4.15-6.15 Place: Room 7314, CUNY Graduate Center Speaker: Dongwoo Kim (CUNY) Title: Explanation and Modality: On Why The Swampman Is Still Worrisome to Teleosemanticists
Abstract: Many have thought that Davidson’s Swampman scenario offers a serious problem to teleosemantics. For it appears to be possible from the scenario that there are completely ahistorical creatures with beliefs, and this apparent possibility contradicts the theory. In a series of papers (2001, 2006, 2016), Papineau argues that the Swampman scenario is not even the start of an objection to teleosemantics as a scientific reduction of belief. It is against this claim that I want to argue here. I shall argue that the explanatory power of teleosemantics rests on two conceptual pillars, namely success semantics and the etiological conception of biological function, and that the Swampman scenario questions the adequacy of the foundational conceptual commitments. Along the way, some general connection between explanation and modality will be developed that sheds a new light on Kripke’s analysis of necessary a posteriori propositions. The conclusion will be that teleosemanticists should tackle the Swampman objection head on.
- - - - Tuesday, Oct 8, 2019 - - - -
- - - - Wednesday, Oct 9, 2019 - - - -
- - - - Thursday, Oct 10, 2019 - - - -
New York Category Theory Seminar
Department of Computer Science, Department of Mathematics The Graduate Center of The City University of New York
Date and Time: Thursday October 10, 2019, 7:00 - 8:30 PM., Room 6417. (NOTICE SPECIAL DAY)
Speaker: Jonathan Weinberger, TU Darmstadt.
Title: Towards complete spreads for higher toposes.
Abstract: The concept of a spread of topological spaces introduced and investigated by Fox (1957) and Michael (1963) provides a fruitful notion of branched covering with (well-behaved) singularities.
Bunge and Funk, partially in joint work with Carboni, Jibladze, Lack, Niefield and Streicher, have developed a theory of (complete) spreads over (1-)toposes (most notably in the period 1995--2005). In particular, there is a precise connection to Lawvere's notion of a distribution on a topos.
We suggest generalizations of some aspects of this theory to (∞,1)-topos theory. Of particular interest are higher versions of the symmetric topos, as well as the hyperpure, complete spread factorization system. Besides working with Lurie's notion of Grothendieck (∞,1)-topos, we also present an outlook on using more general notions of higher toposes, such as currently proposed notions of elementary (∞,1)-toposes due to Anel--Biederman--Joyal--Finster, Rasekh, and Shulman.
- - - - Friday, Oct 11, 2019 - - - -
Set Theory Seminar CUNY Graduate Center, Room 6417 Friday, October 11, 10:00-11:45am Kaethe Minden, Bard College TBA
Logic Workshop CUNY Graduate Center, Room 6417 Friday, October 11, 2:00-3:30pm Miha Habič, Bard College TBA
Seminar in Logic, Games and Language CUNY Graduate Center, Room 4421 Friday, October 11, 4:15-6:15
Arthur Paul Pedersen, Brooklyn College
Bayesian Aggregation under Severe Uncertainty and Unresolved Conflict
Abstract Outline:...1. The problem of External vs Internal Bayesianism: Update then aggregate or aggregate then update? 2. Bayesian Extensions of Arrow's Theorem 3. Incompleteness vs. Indeterminancy (or tentative and assertive incompleteness) 4. Set-Valued Aggregation 5. Dilation 6. Possibility Theorems, Return of Arrow's Theorems
Next Week in Logic at CUNY:
- - - - Monday, Oct 14, 2019 - - - -
- - - - Tuesday, Oct 15, 2019 - - - -
- - - - Wednesday, Oct 16, 2019 - - - -
- - - - Thursday, Oct 17, 2019 - - - -
- - - - Friday, Oct 18, 2019 - - - -
Logic Workshop CUNY Graduate Center, Room 6417 Friday, October 18, 2:00-3:30pm
Philipp Rothmaler, CUNY
High and low formulas in the model theory of modules
A positive primitive (henceforth pp) formula is an existentially quantified (i.e., a projection of a) finite system of linear equations (over a given associative ring R). In this talk I am interested exclusively in such formulas with one free variable. I call such a formula high if, in every injective module E, it defines all of E. Note, the high formulas form a filter in the lattice of all unary pp formulas. Long time ago I discovered this dichotomy: every (unary) pp formula is either high or else bounded (but not both), which means that there is a nonzero ring element that annihilates, in every module, all of the set defined by the formula (which is, in fact, an additive subgroup of the module).
I had not given this much further thought until recently, when I discovered, in collaboration with A. Martsinkovsky, that the dual notion of low formula gives rise to a torsion theory, namely injective torsion as introduce by him and J. Russell in recent work. I call a formula low if it vanishes on the flat modules, or, equivalently, on the ring as a module over itself. Note, the low formulas form an ideal in the lattice of all unary pp formulas. I will explain how elementary duality (as introduced by Prest and Herzog) yields at once another dichotomy: every pp formula is either low or else cobounded (but not both), where this means, dually, that the action of some nonzero ring element sends every module into the subgroup defined by that formula.
Interestingly, these two dichotomies are, in general, completely independent. But I will show how their interplay can be used to characterize (not necessarily commutative) domains within the class of all rings, and one-sided Ore domains and also two-sided Ore domains within all domains. (Commutative domains are two-sided Ore.)
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Maciej Malicki: Continuous logic
IMPAN Working Group in Applications of Set Theory
10/6/2019
Seminar: Working group in applications of set theory, IMPAN
Thursday, 10.10.2019,
Group lunch (optional): meeting at the reception of IMPAN at 12.30, going to www.wieszcozjesz.pl/1-Danie-dnia (the menu will update)
Seminar at 2:15 pm, room 105, IMPAN, Śniadecki 8, Warsaw.
Speaker: Maciej Malicki (Warsaw School of Economics, SGH)
Title: "Continuous logic"
Abstact: "This series of talks will be devoted to a gentle introduction to continuous logic - a natural generalization of first-order logic that is suitable in studying mathematical objects equipped with a metric, e.g. Polish metric spaces and groups, Banach spaces, C*-algebras, etc. Continuous logic is surprisingly parallel to classical logic, and all fundamental concepts such as definable sets, algebraic sets, type spaces, quantifier elimination, omitting types, imaginaries, stability, etc., have their counterparts in this setting.
In the first talk, we will discuss the very basics: metric structures, signatures, connectives and quantifiers, truth values, theories, etc.
Literature: Ben Yaacov, Itai; Berenstein, Alexander; Henson, C. Ward; Usvyatsov, Alexander; Model theory for metric structures. Model theory with applications to algebra and analysis. Vol. 2, 315--427, London Math. Soc. Lecture Note Ser., 350, Cambridge Univ. Press, Cambridge, 2008.".
Visit our seminar webpage which may include announcements of some future talks at https://www.impan.pl/~set_theory/Seminar/
Cheers, Piotr.
Tagged: Maciej Malicki
Wednesday seminar
Prague Set Theory Seminar
10/3/2019
Dear all,
The seminar meets on Wednesday October 9th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: David Chodounsky -- Generic Ultrafilters
S. Todorcevic proved that selective ultrafilters are (assuming certain
large cardinal hypothesis) exactly filters generic on P(omega)/fin over
the model L(R). We (with J. Zapletal) provide a combinatorial
characterization of filters generic on P(omega)/I for F_sigma ideals I,
generalizing the result of Todorcevic.
Best,
David
Tagged: David Chodounsky
UPDATE: This Week in Logic at CUNY
This Week in Logic at CUNY
10/2/2019
Hi everyone,
Please note that this Friday's Set Theory Seminar has been cancelled (rescheduled for 11/22).
Best regards,
Jonas
This Week in Logic at CUNY:
- - - - Monday, Sep 30, 2019 - - - -
- - - - Tuesday, Oct 1, 2019 - - - -
- - - - Wednesday, Oct 2, 2019 - - - -
MOPA (Models of Peano Arithmetic) CUNY Graduate Center, Room 4213.03 (Math Thesis Room) Wednesday, October 2, 6:30-8:00pm Corey Switzer, CUNY Constructions of Size Continuum
I will give an exposition of a technique by Baldwin and Laskowski for extending the Henkin construction to get models of size continuum with interesting properties. The main theorem gives sufficient conditions for a theory to have a model of size continuum which is Borel, atomic and omits some given collection of countably many types. Time permitting I will sketch some applications as well.
- - - - Thursday, Oct 3, 2019 - - - -
- - - - Friday, Oct 4, 2019 - - - -
Set Theory Seminar CUNY Graduate Center, Room 6417 Friday, October 4, 10:00-11:45am
(TALK CANCELLED - RESCHEDULED FOR 11/22)
Model Theory Seminar CUNY Graduate Center, Room 6417 Friday, October 4, 12:30-2:00pm
Alexander Van Abel, CUNY On Pseudofinite Dimension and Measure
A pseudofinite structure is (among many equivalent definitions) a structure which is elementarily equivalent to an infinite ultraproduct of finite structures. In this talk, we discuss how the natural counting measure on finite structures lifts to useful notions of dimension and measure on pseudofinite structures. We give a proof of Furstenburg's Correspondence Principle in combinatorial number theory, using pseudofinite measure. We sketch a proof, by Chernikov and Starchenko, of a special case ('stable' graphs) of the Erdös-Hajnal conjecture, using a particular notion of pseudofinite dimension. Finally, we discuss how a different notion of dimension leads to simplicity results. This talk is largely based on Darío García's lecture notes on 'Model theory of pseudofinite structures'.
Logic Workshop
CUNY Graduate Center, Room 6417
Friday, Oct 4, 2:00-3:30pm
Hans Schoutens, CUNY All your favorite Taylor series wrapped up in a nice little package: the ring of 'catanomials'.
The nice little package is a regular, existentially closed, Henselian local subring of the ring of (formal) power series over your favorite field (R, C, Q?). Moreover, this ring is closed under derivations, anti-derivations, composition, etc. The favorite series (in a single variable, say) include all algebraic functions, all elementary functions, all hypergeometrical functions, all holonomic functions (i.e., solutions of a linear, algebraic ODE), etc.
The way to obtain these is by looking at some non-standard model of the theory of polynomial rings, and then defining its 'catanomials' as the truncations of these functions by only looking at its finite degree terms. In the special case that the non-standard model is an ultrapower of the polynomial ring, the resulting algebra, called the catapower, is just the full power series ring. Whereas the latter may sound less glorious, we can nonetheless do better by taking different non-standard models. Enters the embedded model of PA* of such a model and its standard systems!
Seminar in Logic, Games and Language Friday, October 4, 2019, 4:15 PM, room 4421 Jia Xu, Hunter College New Directions in Neural Machine Translation
Neural Machine Translation (NMT) is an end-to-end learning approach for automated human language translation. With the advance of the Attentional Neural Networks, NMT has achieved tremendous success. We introduce a powerful approach to further boost Neural Machine Translation (NMT). We view social interaction as a computational device that generates pre-computed knowledge by human interaction throughout the language evolution. Our experimental verification overwhelmingly supports our theory. On six different language directions, we have achieved up to 10% relative improvement in machine translation quality.
Next Week in Logic at CUNY:
- - - - Monday, Oct 7, 2019 - - - -
- - - - Tuesday, Oct 8, 2019 - - - -
- - - - Wednesday, Oct 9, 2019 - - - -
- - - - Thursday, Oct 10, 2019 - - - -
New York Category Theory Seminar
Department of Computer Science, Department of Mathematics The Graduate Center of The City University of New York
Date and Time: Thursday October 10, 2019, 7:00 - 8:30 PM., Room 6417. (NOTICE SPECIAL DAY)
Speaker: Jonathan Weinberger, TU Darmstadt.
Title: Towards complete spreads for higher toposes.
Abstract: The concept of a spread of topological spaces introduced and investigated by Fox (1957) and Michael (1963) provides a fruitful notion of branched covering with (well-behaved) singularities.
Bunge and Funk, partially in joint work with Carboni, Jibladze, Lack, Niefield and Streicher, have developed a theory of (complete) spreads over (1-)toposes (most notably in the period 1995--2005). In particular, there is a precise connection to Lawvere's notion of a distribution on a topos.
We suggest generalizations of some aspects of this theory to (∞,1)-topos theory. Of particular interest are higher versions of the symmetric topos, as well as the hyperpure, complete spread factorization system. Besides working with Lurie's notion of Grothendieck (∞,1)-topos, we also present an outlook on using more general notions of higher toposes, such as currently proposed notions of elementary (∞,1)-toposes due to Anel--Biederman--Joyal--Finster, Rasekh, and Shulman.
- - - - Friday, Oct 11, 2019 - - - -
Set Theory Seminar CUNY Graduate Center, Room 6417 Friday, October 11, 10:00-11:45am Kaethe Minden, Bard College TBA
Logic Workshop CUNY Graduate Center, Room 6417 Friday, October 11, 2:00-3:30pm Miha Habič, Bard College TBA
- - - - Other Logic News - - - -
Princeton has a philosophy of maths group run by Sylvia De Toffoli. All are welcome. Speakers for this semester, and Sylvia's address if you want to be added to the mailing list, are below.
Here is the program for the fall: Time: 4pm-5:30pm Place: 201 Marx Hall, Philosophy Department, Princeton University
09/13 — John Sullivan (TU-Berlin) 09/20 — Silvia De Toffoli (Princeton) 09/27 — Juliette Kennedy (University of Helsinki / visiting at the IAS in Princeton) 10/25 — Keith Weber (Rutgers) 12/06 — Mark Colyvan (University of Sydney) 12/13 — David Dunning (Princeton)
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
(KGRC) talk in the research seminar October 10
Kurt Godel Research Center
10/1/2019
The KGRC welcomes Jana Marikova, Clifton Ealy, Alexander Osipov, Christina
Brech, Masahiko Sato, István Juház, Miguel Moreno and Mohammad Golshani as
guests. Professor Marikova (host: Benjamin Miller) will stay util June 30,
2020 and give a talk on November 7. Professor Ealy (host: Benjamin Miller)
will stay until June 30, 2020 and give a talk on October 3. Dr. Osipov
(host: Lyubomyr Zdomskyy) will stay until Oktober 12. Professor Brech
(host: Lyubomyr Zdomskyy) will stay until October 12 and give a talk on
October 10 (see below). Professor Sato (host: Sy-David Friedman) will stay
from October 6 to October 9. Dr. Moreno (host: Lyubomyr Zdomskyy) will
stay from December 1, 2019 to November 30, 2020. Dr. Golshani (hosts:
Sy-David Friedman, Yair Hayut) will stay from December 4, 2019 to December
11, 2019 and give a talk on December 5.
* * *
Research seminar
Kurt Gödel Research Center
Thursday, October 10
"Isometries of combinatorial Banach spaces"
Christina Brech
(Universidade de São Paulo, Brazil)
The Schreier family $\mathcal{S} = \{F \in [\omega]^{<\omega}: |F| \leq
\min+1\}$ induces a structure with no infinite sets of indiscernibles and this
can be generalized to the context of Banach spaces. The fact that the canonical
basis of the Banach space induced by the Schreier family doesn't have infinite
indiscernibles gives a hint on the rigidity of this object, that is, on the
fact that isometries of the space fix the basis, up to signs.
In this talk, we will give the background for the previous paragraph and will
present a generalized version of it, obtained in a joint work with V. Ferenczi
and A. Tcaciuc: given a regular family $\mathcal{F}$, it is possible to define
its corresponding combinatorial space $X_\mathcal{F}$, which is a Banach space
whose norm is defined in terms of the family $\mathcal{F}$. We prove that every
isometry of a combinatorial Banach space $X_\mathcal{F}$ is induced by a signed
permutation of its canonical basis.
Time and Place
Tea at 3:30pm in the KGRC meeting room
Talk at 4:00pm in the KGRC lecture room
Universität Wien
Institut für Mathematik
Kurt Gödel Research Center
Seminar room SR D5.48
Augasse 2-6, UZA 1 - Building 2
1090 Wien
Logic Seminar 3 Oct 2019 17:00 hrs at NUS
NUS Logic Seminar
9/30/2019
Invitation to the Logic Seminar at the National University of Singapore
Date: Thursday, 3 October 2019, 17:00 hrs
Room: S17#06-11, Department of Mathematics, NUS
Speaker: Dilip Raghavan
Title: All ultrafilters in L(R)[U] are rapid.
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: We will show that all ultrafilters in the model L(R)[U] are rapid.
This is joint work with Paul Larson.
Tagged: Dilip Raghavan
This Week in Logic at CUNY
This Week in Logic at CUNY
9/30/2019
This Week in Logic at CUNY:
- - - - Monday, Sep 30, 2019 - - - -
- - - - Tuesday, Oct 1, 2019 - - - -
- - - - Wednesday, Oct 2, 2019 - - - -
MOPA (Models of Peano Arithmetic) CUNY Graduate Center, Room 4213.03 (Math Thesis Room) Wednesday, October 2, 6:30-8:00pm Corey Switzer, CUNY Constructions of Size Continuum
I will give an exposition of a technique by Baldwin and Laskowski for extending the Henkin construction to get models of size continuum with interesting properties. The main theorem gives sufficient conditions for a theory to have a model of size continuum which is Borel, atomic and omits some given collection of countably many types. Time permitting I will sketch some applications as well.
- - - - Thursday, Oct 3, 2019 - - - -
- - - - Friday, Oct 4, 2019 - - - -
Set Theory Seminar CUNY Graduate Center, Room 6417 Friday, October 4, 10:00-11:45am
Brent Cody, Virginia Commonwealth University A refinement of the Ramsey hierarchy via indescribability
A subset XX of a cardinal κκ is Ramsey if for every function f:[X]<ωo2f:[X]<ωo2 there is a set H⊆XH⊆X of cardinality κκ which is homogeneous for ff, meaning that f↾[H]nf↾[H]n is constant for each n<ωn<ω. Baumgartner proved that if κκ is Ramsey, then the collection of non-Ramsey subsets of κκ is a normal ideal on κκ. We will discuss some recent results concerning Ramsey properties in which homogeneous sets are demanded to be indescribable of a particular degree. Moreover, by iterating Feng's Ramsey operator, which he used to define a notion of αα-Ramseyness of a cardinal κκ, we will consider hypotheses in which homogeneous sets themselves satisfy various Ramsey properties. For ordinals α,β<κα,β<κ we will define a notion of αα-Π1βΠβ1-Ramseyness of a cardinal κκ where αα indicates how many times the Ramsey operator has been iterated and ββ indicates the degree of transfinite indescribability (due to Sharpe-Welch and independently Bagaria) one initially demands homogeneous to satisfy. We will prove that for α,β<κα,β<κ an αα-Π1βΠβ1-Ramsey cardinal is strictly between Feng's αα-Ramsey and an (α+1α+1)-Ramsey cardinal in consistency strength. Moreover, for fixed α<κα<κ, as ββ increases the αα-Π1βΠβ1-Ramsey cardinals yield a strictly increasing hierarchy, in a somewhat subtle sense. For β0<β1<κβ0<β1<κ and for large enough α<κα<κ, κκ being αα-Π1β0Πβ01-Ramsey is equivalent to κκ being αα-Π1β1Πβ11-Ramsey (we will identify the least αα at which this equivalence occurs). But if α,β0<κα,β0<κ there is a large enough β1<κβ1<κ such that κκ being αα-Π1β0Πβ01-Ramsey is strictly weaker than κκ being αα-Π1β1Πβ11-Ramsey. All of these results seem to require a careful analysis of the ideals associated to the various large cardinal notions.
Model Theory Seminar CUNY Graduate Center, Room 6417 Friday, October 4, 12:30-2:00pm
Alexander Van Abel, CUNY On Pseudofinite Dimension and Measure
A pseudofinite structure is (among many equivalent definitions) a structure which is elementarily equivalent to an infinite ultraproduct of finite structures. In this talk, we discuss how the natural counting measure on finite structures lifts to useful notions of dimension and measure on pseudofinite structures. We give a proof of Furstenburg's Correspondence Principle in combinatorial number theory, using pseudofinite measure. We sketch a proof, by Chernikov and Starchenko, of a special case ('stable' graphs) of the Erdös-Hajnal conjecture, using a particular notion of pseudofinite dimension. Finally, we discuss how a different notion of dimension leads to simplicity results. This talk is largely based on Darío García's lecture notes on 'Model theory of pseudofinite structures'.
Logic Workshop
CUNY Graduate Center, Room 6417
Friday, Oct 4, 2:00-3:30pm
Hans Schoutens, CUNY All your favorite Taylor series wrapped up in a nice little package: the ring of 'catanomials'.
The nice little package is a regular, existentially closed, Henselian local subring of the ring of (formal) power series over your favorite field (R, C, Q?). Moreover, this ring is closed under derivations, anti-derivations, composition, etc. The favorite series (in a single variable, say) include all algebraic functions, all elementary functions, all hypergeometrical functions, all holonomic functions (i.e., solutions of a linear, algebraic ODE), etc.
The way to obtain these is by looking at some non-standard model of the theory of polynomial rings, and then defining its 'catanomials' as the truncations of these functions by only looking at its finite degree terms. In the special case that the non-standard model is an ultrapower of the polynomial ring, the resulting algebra, called the catapower, is just the full power series ring. Whereas the latter may sound less glorious, we can nonetheless do better by taking different non-standard models. Enters the embedded model of PA* of such a model and its standard systems!
Seminar in Logic, Games and Language Friday, October 4, 2019, 4:15 PM, room 4421 Jia Xu, Hunter College New Directions in Neural Machine Translation
Neural Machine Translation (NMT) is an end-to-end learning approach for automated human language translation. With the advance of the Attentional Neural Networks, NMT has achieved tremendous success. We introduce a powerful approach to further boost Neural Machine Translation (NMT). We view social interaction as a computational device that generates pre-computed knowledge by human interaction throughout the language evolution. Our experimental verification overwhelmingly supports our theory. On six different language directions, we have achieved up to 10% relative improvement in machine translation quality.
Next Week in Logic at CUNY:
- - - - Monday, Oct 7, 2019 - - - -
- - - - Tuesday, Oct 8, 2019 - - - -
- - - - Wednesday, Oct 9, 2019 - - - -
- - - - Thursday, Oct 10, 2019 - - - -
New York Category Theory Seminar
Department of Computer Science, Department of Mathematics The Graduate Center of The City University of New York
Date and Time: Thursday October 10, 2019, 7:00 - 8:30 PM., Room 6417. (NOTICE SPECIAL DAY)
Speaker: Jonathan Weinberger, TU Darmstadt.
Title: Towards complete spreads for higher toposes.
Abstract: The concept of a spread of topological spaces introduced and investigated by Fox (1957) and Michael (1963) provides a fruitful notion of branched covering with (well-behaved) singularities.
Bunge and Funk, partially in joint work with Carboni, Jibladze, Lack, Niefield and Streicher, have developed a theory of (complete) spreads over (1-)toposes (most notably in the period 1995--2005). In particular, there is a precise connection to Lawvere's notion of a distribution on a topos.
We suggest generalizations of some aspects of this theory to (∞,1)-topos theory. Of particular interest are higher versions of the symmetric topos, as well as the hyperpure, complete spread factorization system. Besides working with Lurie's notion of Grothendieck (∞,1)-topos, we also present an outlook on using more general notions of higher toposes, such as currently proposed notions of elementary (∞,1)-toposes due to Anel--Biederman--Joyal--Finster, Rasekh, and Shulman.
- - - - Friday, Oct 11, 2019 - - - -
Set Theory Seminar CUNY Graduate Center, Room 6417 Friday, October 11, 10:00-11:45am Kaethe Minden, Bard College TBA
Logic Workshop CUNY Graduate Center, Room 6417 Friday,
October 11, 2:00-3:30pm Miha Habič, Bard College TBA
- - - - Other Logic News - - - -
Princeton has a philosophy of maths group run by Sylvia De Toffoli. All are welcome. Speakers for this semester, and Sylvia's address if you want to be added to the mailing list, are below.
Here is the program for the fall: Time: 4pm-5:30pm Place: 201 Marx Hall, Philosophy Department, Princeton University
09/13 — John Sullivan (TU-Berlin) 09/20 — Silvia De Toffoli (Princeton) 09/27 — Juliette Kennedy (University of Helsinki / visiting at the IAS in Princeton) 10/25 — Keith Weber (Rutgers) 12/06 — Mark Colyvan (University of Sydney) 12/13 — David Dunning (Princeton)
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Winfried Just: What does a former set theorist do in mathematical biology?
Toronto Set Theory Seminar
9/29/2019
Place: Fields Institute (Room 210)
Date: October 4, 2019 (13:30-15:00)
Speaker: Winfried Just
Title: What does a former set theorist do in mathematical biology?
Abstract:
This presentation aims at illustrating what could a a set-theorist's point
of view contribute to the exploration of mathematical models of biological
systems.
\smallskip
These models usually take the form of highly complex dynamical systems.
One standard measure of the complexity of such a system is
\emph{topological entropy $h$.}
Two of the textbook definitions of this notion look like this:
\begin{equation*}
h = \lim_{\eps \rightarrow 0^+}\limsup_{T \rightarrow \infty} \frac{\ln
sep(\eps, d_T)}{T} \quad \mbox{and} \quad h = \lim_{\eps \rightarrow
0^+}\limsup_{T \rightarrow \infty} \frac{\ln span(\eps, d_T)}{T}.
\end{equation*}
They were proposed around 1970 independently by Bowen and Dinaburg.
\smallskip
An obvious question is whether we can replace \emph{lim sup} in this
definition by \emph{lim.} One would expect that there should have been a
known counterexample by now.
But there wasn't, until the presenter and his former Ph.D. student Dr.
Ying Xin constructed one in 2017.
\smallskip
The construction was inspired by some techniques that the presenter
remembered from his time in the Toronto Set Theory Seminar.
Tagged: Winfried Just
Wednesday seminar
Prague Set Theory Seminar
9/26/2019
Dear all,
The seminar meets on Wednesday October 2nd at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Noé de Rancourt -- Weakly Ramsey ultrafilters
An ultrafilter on omega is (n, k)-weakly Ramsey if for every colouring
of n-elements subsets of omega with finitely many colours, there exists
an element in the ultrafilter that meets at most k colours. In the same
way that Ramsey ultrafilters are minimal in the Rudin-Keisler ordering,
Jonathan Verner proved that weakly Ramsey ultrafilters are low in this
ordering: there is no infinite chains below them.
After presenting his proof, I will prove that the converse is not true.
Surprisingly, the construction of the counterexample combines forcing
with the use of finite combinatorics; namely, a Ramsey theorem for
finite graphs by Nešetřil and Rödl.
Best,
David
Tagged: Noé de Rancourt
Shai Ben-David: A basic machine learning problem is independent of set theory
Toronto Set Theory Seminar
9/25/2019
Place: Fields Institute (Room 210)
Date: September 27, 2019 (13:30-15:00)
Speaker: Shai Ben-David
Title: A basic machine learning problem is independent of set theory
Abstract:
The mathematical foundations of machine learning play a key role in the
development of the field. They improve our understanding and provide tools
for designing new learning paradigms. The advantages of mathematical
analysis, however, sometimes come with a cost. Gödel and Cohen showed, in
a nutshell, that not everything is provable. Here we show that machine
learning shares this fate. We describe simple scenarios where learnability
cannot be proved nor refuted using the standard axioms of mathematics. Our
proof is based on the fact the continuum hypothesis cannot be proved nor
refuted. We show that, in some cases, a solution to the ‘estimating the
maximum expectation’ problem is equivalent to the continuum hypothesis.
As a corollary, we show that for some basic notion of statistical learning
there can be no combinatorial dimension that characterizes learnability
(in a way similar to the fundamental
characterization of PAC learnability by VC-dimension).
The talk is based on joint work with Pavel Hrubeˇs, Shay Moran, Amir
Shpilka, and Amir Yehudayoff
Tagged: Shai Ben-David
(KGRC) talk in the research seminar NEXT week, September 3
Kurt Godel Research Center
9/23/2019
The KGRC welcomes Jana Marikova, Clifton Ealy, Alexander Osipov, Masahiko
Sato, Christina Brech and Miguel Moreno as guests. Professor Marikova
(host: Benjamin Miller) will stay util June 30, 2020 and give a talk on
November 7. Professor Ealy (host: Benjamin Miller) will stay until June
30, 2020 and give a talk on October 3 (see below). Dr. Osipov (host:
Lyubomyr Zdomskyy) will stay until Oktober 12. Professor Sato (host:
Sy-David Friedman) will stay from Oktober 6 to October 9. Professor Brech
(host: Lyubomyr Zdomskyy) will stay from September 29 to Oktober 12 and
give a talk on October 10. Dr. Moreno will (host: Lyubomyr Zdomskyy) will
stay from December 1, 2019 to November 30, 2020.
* * *
Research seminar
Kurt Gödel Research Center
Thursday, October 3
"Residue field domination in real closed valued fields"
Clifton Ealy
(Western Illinois University, Macomb, USA)
I will talk about some recent results in the model theory of valued
fields. No knowledge of valued fields or model theory will be assumed.
Haskell, Hrushovski, and Macpherson show that in an algebraically closed
valued field, the residue field and the value group control the rest of
the structure: $tp(L/Ck(L)\Gamma(L)$ will have a unique extension to
$M\supseteq C$, as long as the residue field, $k(L)$, and value group,
$\Gamma(L)$, of $L$ are independent from those of $M$ (and as long as $C$
is maximal).
This behavior is striking, because it is what typically occurs in a stable
structure (where types over algebraically closed sets have unique
extensions to independent sets) but valued fields are far from stable, due
to the order on the value group.
Real closed valued fields are even further from stable since the main sort
is ordered. One might expect the analogous theorem about real closed
valued fields to be that $tp(L/M)$ is implied by $tp(L/Ck(L)\Gamma(L))$
together with the order type of $L$ over $M$. In fact we show that the
order type is unnecessary, that just as in the algebraically closed case,
one has that $tp(L/M)$ is implied by $tp(L/k(L)\Gamma(L))$.
This is joint work with Haskell and Marikova.
Time and Place
Universität Wien
Institut für Mathematik
Kurt Gödel Research Center
Seminar room D5.48
Augasse 2-6, UZA 1 - Building 2
1090 Wien
Tea at 3:30pm in the KGRC meeting room
Talk at 4:00pm in the KGRC lecture room
Catania Set Theory and Topology Conference, February 18-21, 2020
Conference
9/23/2019
We're glad to announce the Catania Set Theory and Topology Conference, which will take place at the University of Catania in Italy, February 18-21 2020. Registration is now open at: https://sites.google.com/view/cs2t/home
Our conference aims to bring together researchers and students working on set theory and its applications to a wide spectrum of areas of mathematics, and in particular to Topology, to discuss the most recent advances and main open problems in the field and foster collaboration. There will be eight invited lectures and each of the participants can contribute a 20-30 minute talk.
TOPICS: set theoretic topology, forcing, large cardinals, descriptive set theory, PCF theory, cardinal invariants.
INVITED SPEAKERS
Leandro Aurichi (University of São Paulo-São Carlos, Brazil)
Joan Bagaria (University of Barcelona, Spain)
István Juhász (Hungarian Academy of Sciences, Hungary)
Menachem Kojman (Ben Gurion University, Israel)
Menachem Magidor (Hebrew University of Jerusalem, Israel)
Gianluca Paolini (University of Turin, Italy)
Stevo Todorcevic (University of Toronto, Canada and CNRS, Paris)
Lyubomyr Zdomskyy (Kurt Gödel Research Center, Vienna, Austria)
ORGANIZERS: Angelo Bella, Domenico Cantone and Santi Spadaro (University of Catania).
Tagged: Leandro Aurichi, Joan Bagaria, István Juhász, Menachem Kojman, Menachem Magidor, Gianluca Paolini, Stevo Todorcevic, Lyubomyr Zdomskyy
This Week in Logic at CUNY
This Week in Logic at CUNY
9/22/2019
This Week in Logic at CUNY:
- - - - Monday, Sep 23, 2019 - - - -
Logic and Metaphysics Workshop Date: Monday, September 23rd, 4.15-6.15 Place: Room 7314, CUNY Graduate Center Speaker: Alessandro Rossi (St Andrews) Title: Existence, Verbal Disputes and Equivocation
Abstract: Noneism is the theory according to which some things do not exist. Following an established convention, I will call allism the negation of noneism (every thing exists). Lewis [1990] and, more recently, Woodward [2013] argued that the allism/noneism dispute turns on an equivocation about the meaning of ‘exists’ and would thereby be merely verbal. These arguments have been attacked by Priest [2005, 2011, 2013], who took the dispute to be genuine. In this paper, I will present two new arguments for the genuineness of the allism/noneism dispute. The first appeals to a recent version of logical pluralism defended by Kouri Kissel [Forth]: the two parties could be seen as engaging in a metalinguistic negotiation, that is, a normative disagreement about which meaning of ‘exists’ is best suited for a certain domain of discourse. Secondly, Williamson [1987] indicated a proof-theoretic criterion the two sides should meet in order for their dispute to count as genuine: they must share enough rules of inference governing ‘exist’ to characterise it up to logical equivalence. This challenge, I argue, can be met.
- - - - Tuesday, Sep 24, 2019 - - - -
Computational Logic Seminar Tuesday, September 24, Time 2:00 - 4:00 PM
CUNY Graduate Center, Room 5382 Speaker: John Connor, Graduate Center Title: Dual Intuitionistic Epistemic Logic
Abstract: Intuitionistic logic, along with the informal "proof semantics" given by the Brouwer–Heyting–Kolmogorov interpretation, can be dualized; yielding dual-intuitionistic logic and a "refutation semantics". We will present natural deduction rules for both intuitionistic epistemic logic and dual-intuitionistic logic, and then show how the rules for the dual to the intuitionistic knowledge modality can be derived. If time permits we will discuss an open problem relating to the categorical semantics of dual intuitionisitc logic and the role that the knowledge modality plays there.
- - - - Wednesday, Sep 25, 2019 - - - -
- - - - Thursday, Sep 26, 2019 - - - -
- - - - Friday, Sep 27, 2019 - - - -
Model Theory Seminar CUNY Graduate Center, Room 6417 Friday, September 27, 12:30-2:00pm
Sam Braunfeld, University of Maryland Monadic stability and growth rates of omega-categorical structures
Generalizing the classical combinatorial problem of counting the orbits of a group acting on a finite set, we consider the growth rate of an omega-categorical structure M, which counts the orbits of Aut(M) acting on n-sets. We show that for stable M, there is a gap from subexponential to superexponential growth, corresponding to whether M is monadically stable. This allows us to confirm some longstanding conjectures of Macpherson about the spectrum of possible growth rates.
Logic Workshop
CUNY Graduate Center, Room 6417
Friday, September 27, 2:00-3:30pm
Alf Dolich, CUNY
Tame Expansions of Presburger Arithmetic Over the last several decades a robust theory of 'tame' expansions of the real field has been developed. Typically tameness in manifested in such situations by the definable sets having some particularly simple topological type. In this talk I will consider how this machinery can be adapted to expansions of Presburger arithmetic in which such topological considerations are largely irrelevant. This is joint work with Chris Miller.
Seminar in Logic, Games and Language
CUNY Graduate Center, Room 4421
Friday, September 27, 4:15-6:15
Ignacio Ojea Quintana, Australian National University
Segregating and Integrating Dynamics in Social Networks
Abstract: This talk provides an explanation for online segregation and integration by extending some ideas originally developed by Schelling [1969,1971,2006]. Agents in a social network aim to satisfy homophily and heterophily thresholds but, unlike other Schelling-like models, they do not change location within at topology but they cut and form new ties with neighbors. Hence the model is designed to represent the dynamics of friending/unfriending and following/unfollowing in social media. Although it is different from Schelling's, the model reveals that high degrees of macro segregation (integration) can emerge even with moderate homophily (heterophily) preferences at the micro level. We also show that heterophily has more effect than homophily in unequal populations. These results are demonstrated via simulations using Netlogo, and some convergence properties are proved analytically. The upshot, much like in Schelling's original models, is that online tribalism is cheap and that individual behavior can have an unexpected large effect at the macro level.
NB. 1) Dr. Ignacio Quintana received his doctorate from Columbia University. 2) Thomas Schelling won the Nobel Prize in Economics in 2005.
Next Week in Logic at CUNY:
- - - - Monday, Sep 30, 2019 - - - -
- - - - Tuesday, Oct 1, 2019 - - - -
- - - - Wednesday, Oct 2, 2019 - - - -
- - - - Thursday, Oct 3, 2019 - - - -
- - - - Friday, Oct 4, 2019 - - - -
Set Theory Seminar CUNY Graduate Center, Room 6417 Friday, October 4, 10:00-11:45am
Brent Cody, Virginia Commonwealth University TBA
Logic Workshop
CUNY Graduate Center, Room 6417
Friday, Oct 4, 2:00-3:30pm
Hans Schoutens, CUNY All your favorite Taylor series wrapped up in a nice little package: the ring of 'catanomials'.
The nice little package is a regular, existentially closed, Henselian local subring of the ring of (formal) power series over your favorite field (R, C, Q?). Moreover, this ring is closed under derivations, anti-derivations, composition, etc. The favorite series (in a single variable, say) include all algebraic functions, all elementary functions, all hypergeometrical functions, all holonomic functions (i.e., solutions of a linear, algebraic ODE), etc.
The way to obtain these is by looking at some non-standard model of the theory of polynomial rings, and then defining its 'catanomials' as the truncations of these functions by only looking at its finite degree terms. In the special case that the non-standard model is an ultrapower of the polynomial ring, the resulting algebra, called the catapower, is just the full power series ring. Whereas the latter may sound less glorious, we can nonetheless do better by taking different non-standard models. Enters the embedded model of PA* of such a model and its standard systems!
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Daniel Calderón: Can you take Akemann--Weaver's $\diamondsuit$ away?
Toronto Set Theory Seminar
9/19/2019
Place: Fields Institute (Room 210)
Date: , 2019 (13:30-15:00)
Speaker: Daniel Calderón
Title: Can you take Akemann--Weaver's $\diamondsuit$ away?
Abstract:
Let $\sK(H)$ be the $\C$-algebra of compact operators on a complex
Hilbert space $H$. In 1948, Naimark proved that the representation theory
of $\sK(H)$ is as easy as possible, and some years later, he asked whether
this property characterizes $\sK(H)$ as a $\C$-algebra. Informally, a
\textit{counterexample to Naimark's Problem} is a $\C$-algebra whose
representation theory is extremely easy but is not isomorphic to any
algebra of compact operators.\\
It was not until 2004 when, assuming that $\diamondsuit$ holds, Akemann
and Weaver exhibited the first counterexample to Naimark's Problem. All
known counterexamples to Naimark's Problem has been constructed using some
modification of the technique introduced by Akemann and Weaver, and it was
not known whether $\diamondsuit$ was a necessary hypothesis to assure the
existence of such a $\C$-algebra. In recent work with Ilijas Farah we give
an answer to this question.
Tagged: Daniel Calderón
This Week in Logic at CUNY
This Week in Logic at CUNY
9/15/2019
This Week in Logic at CUNY:
- - - - Monday, Sep 16, 2019 - - - -
Logic and Metaphysics Workshop Date: Monday, September 16th, 4.15-6.15 Place: Room 7314, CUNY Graduate Center Speaker: Ole Hjortland and Ben Martin (Bergen) Title: Anti-Exceptionalism and Explanations in Logic
Abstract: According to logical anti-exceptionalism we come to be justified in believing logical theories by similar means to scientific theories. This is often explained by saying that theory choice in logic proceeds via abductive arguments (Priest, Russell, Williamson, Hjortland). Thus, the success of classical and non-classical theories of validity are compared by their ability to explain the relevant data. However, as of yet there is no agreed upon account of which data logical theories must explain, and subsequently how they prove their mettle. In this paper, we provide a non-causal account of logical explanation, and show how it can accommodate important disputes about logic.
- - - - Tuesday, Sep 17, 2019 - - - -
Computational Logic Seminar Tuesday, September 17, Time 2:00 - 4:00 PM Room 5382 Speaker: Sergei Artemov, Graduate Center Title: Unknown Worlds
Epistemic modal logic views an epistemic situation as a collection of possible worlds - maximal consistent sets of propositions - with conventional accessibility relations whatever agent i knows in u is true in v. Contrary to the popular belief, such a structure is not necessarily a Kripke model - a standard starting point for epistemic analysis. To be a Kripke model, it should satisfy an additional fully explanatory condition -- a propositional form of common knowledge of the model - and this hidden assumption limits the scope of Kripke modeling in epistemology.
We sketch a theory of epistemic models, EM, in their full generality without assuming common knowledge of the model. We argue for conceptual and practical value of new models for representing knowledge, awareness, and ignorance.
- - - - Wednesday, Sep 18, 2019 - - - -
MOPA (Models of Peano Arithmetic) CUNY Graduate Center, Room 4213.03 (Math Thesis Room) Wednesday, September 18, 6:30-8:00pm Alf Dolich, CUNY Henkin Constructions of Models with Size Continuum after Baldwin and Laskowski In recent work Baldwin and Laskowski introduced a method to construct via a Henkin-style construction models of size continuum in countable many steps. This construction has multiple applications. In this talk I will survey, following a lecture of Baldwin, some of the background and motivations for this construction.
- - - - Thursday, Sep 19, 2019 - - - -
- - - - Friday, Sep 20, 2019 - - - -
Set Theory Seminar
CUNY Graduate Center, Room 6417
Friday, September 20, 10:00-11:45am
Sam Coskey, Boise State University Jumps of equivalence relations and scattered linear orders
This is joint work with John Clemens. We will begin this talk by discussing the problem of classifying the countable scattered linear orders. Here a linear order is called scattered if the rational order doesn’t embed into it. The class of such orders admits a ranking function valued in the ordinals; we will study the corresponding classification problem for each fixed rank. We will show that each increase in rank results in a “jump” in the complexity of the classification problem. In the second part of the talk we will define a family of jump operators on equivalence relations, each associated with a fixed countable group. The jump in the case of scattered linear orders is that associated with the group Z of integers. We will discuss the basic theory of these jump operators. Finally, we will discuss the question of when such a jump operator is proper, in the sense that the jump of E is strictly above E in the Borel reducibility order.
Model Theory Seminar CUNY Graduate Center, Room 6417 Friday, September 20, 12:30-2:00pm Matěj Konečný, Charles University Extending partial automorphisms of structures
Abstract: This is based on joint work with David Evans, Jan Hubička and Jaroslav Nešetřil. The extension property for partial automorphisms (EPPA), also called the Hrushovski property is a property of classes of finite structures stating that for every A there is B containing A as a substructure such that every isomorphism of substructures of A extends to an automorphism of B. Every class with EPPA is an amalgamation class, in fact, EPPA is equivalent to some properties of the automorphism group of the Fraisse limit of the class. In particular, EPPA is a key ingredient in proving ample generics, the small index property etc. In this talk, we show a new easy way of proving EPPA for the class of all finite graphs and then explain how to extend these techniques to get EPPA for two-graph and also the strongest sufficient condition for EPPA so far. This talk should be self-contained.
Logic Workshop
CUNY Graduate Center, Room 6417
Friday, September 20, 2:00-3:30pm
Artem Chernikov, UCLA N-dependent groups and fields
A first-order theory is n-dependent if the edge relation of an infinite generic (n+1)-hypergraph is not definable in any of its models. N-dependence is a strict hierarchy increasing with n, with 1-dependence corresponding to the well-studied class of NIP theories. I will discuss recent joint work with Nadja Hempel on trying to understand which algebraic structures are n-dependent.
Seminar in Logic, Games and Language
CUNY Graduate Center, Room 4421
Friday, September 20, 4:15-6:15
Arthur Paul Pedersen, Brooklyn College Amartya Sen: Welfare Aggregation and Measurability
Next Week in Logic at CUNY:
- - - - Monday, Sep 23, 2019 - - - -
Logic and Metaphysics Workshop Date: Monday, September 23rd, 4.15-6.15 Place: Room 7314, CUNY Graduate Center Speaker: Alessandro Rossi (St Andrews) Title: Existence, Verbal Disputes and Equivocation
Abstract: Noneism is the theory according to which some things do not exist. Following an established convention, I will call allism the negation of noneism (every thing exists). Lewis [1990] and, more recently, Woodward [2013] argued that the allism/noneism dispute turns on an equivocation about the meaning of ‘exists’ and would thereby be merely verbal. These arguments have been attacked by Priest [2005, 2011, 2013], who took the dispute to be genuine. In this paper, I will present two new arguments for the genuineness of the allism/noneism dispute. The first appeals to a recent version of logical pluralism defended by Kouri Kissel [Forth]: the two parties could be seen as engaging in a metalinguistic negotiation, that is, a normative disagreement about which meaning of ‘exists’ is best suited for a certain domain of discourse. Secondly, Williamson [1987] indicated a proof-theoretic criterion the two sides should meet in order for their dispute to count as genuine: they must share enough rules of inference governing ‘exist’ to characterise it up to logical equivalence. This challenge, I argue, can be met.
- - - - Tuesday, Sep 24, 2019 - - - -
- - - - Wednesday, Sep 25, 2019 - - - -
- - - - Thursday, Sep 26, 2019 - - - -
- - - - Friday, Sep 27, 2019 - - - -
Logic Workshop
CUNY Graduate Center, Room 6417
Friday, September 27, 2:00-3:30pm
Alf Dolich, CUNY TBA
Seminar in Logic, Games and Language
CUNY Graduate Center, Room 4421
Friday, September 27, 4:15-6:15
Ignacio Ojea Quintana, Australian National University
TBA
- - - - Other Logic News - - - -
Theater for the New City presents: Ludwig and Bertie
SEPTEMBER 26 – OCTOBER 13, Thursday, Friday, Saturday at 8PM, Sunday at 3PM
“Ludwig and Bertie” by Douglas Lackey, directed by Alexander Harrington,
takes on the forty-year love/hate relationship between Ludwig Wittgenstein and Bertrand Russell, two leading twentieth-century philosophers, from their first meeting at Cambridge in 1911 to Wittgenstein’s death in 1951.
Aquest missatge, i els fitxers adjunts que hi pugui haver, pot contenir informació confidencial o protegida legalment i s’adreça exclusivament a la persona o entitat destinatària. Si no consteu com a destinatari final
o no teniu l’encàrrec de rebre’l, no esteu autoritzat a llegir-lo, retenir-lo, modificar-lo, distribuir-lo, copiar-lo ni a revelar-ne el contingut. Si l’heu rebut per error, informeu-ne el remitent i elimineu del sistema tant el missatge com els fitxers adjunts
que hi pugui haver.
Este mensaje, y los ficheros adjuntos que pueda incluir, puede contener información confidencial o legalmente protegida y está exclusivamente dirigido a la persona o entidad destinataria. Si usted no consta como destinatario final ni es la persona encargada
de recibirlo, no está autorizado a leerlo, retenerlo, modificarlo, distribuirlo o copiarlo, ni a revelar su contenido. Si lo ha recibido por error, informe de ello al remitente y elimine del sistema tanto el mensaje como los ficheros adjuntos que pueda contener.
This email message and any attachments it carries may contain confidential or legally protected material and are intended solely for the individual or organization to whom they are addressed. If you are not the intended recipient of this message or the person
responsible for processing it, then you are not authorized to read, save, modify, send, copy or disclose any part of it. If you have received the message by mistake, please inform the sender of this and eliminate the message and any attachments it carries
from your account.
Wednesday seminar
Prague Set Theory Seminar
9/12/2019
Dear all,
The seminar meets on Wednesday September 18th at 11:00 in the Institute
of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Jan Grebik -- Dichotomy for actions of tsi Polish groups
I will sketch how to use a variant of G_0 dichotomy to show that the
turbulence dichotomy for Borel orbit equivalence relations is induced by
actions of tsi Polish groups.
Best,
David
Tagged: Jan Grebik
UPDATE: This Week in Logic at CUNY
This Week in Logic at CUNY
9/9/2019
Hi everyone,
Please note the addition of talks in the Computational Logic Seminar (9/10) and the Seminar in Logic, Games, and Language (9/13 and 9/20).
Best,
Jonas Reitz
This Week in Logic at CUNY:
- - - - Monday, Sep 9, 2019 - - - -
Logic and Metaphysics Workshop Spring 2019 Date: Monday, September 9th, 4.15-6.15 Place: Room 7314, CUNY Graduate Center Speaker: Yael Sharvit (UCLA) Title: Temporal ‘de re’ Attitudes
Abstract: A sensible approach to the semantics of tense says that present tense and past tense “refer” to the evaluation time and to some pre-evaluation time, respectively. Indeed, this seems to be the case in unembedded sentences (e.g., Mary is thirty-five, Mary was thirty-five). But embedded tenses seem to misbehave: (1) does not express the proposition that two months prior to s* (= the speech time) Joseph was sure about the truth of [Mary is currently thirty-five]; this proposition is expressed by (2). Assuming that tenses are indexical expressions does not automatically solve the problem, since (1) does not express the proposition that two months prior to s* Joseph was sure about the truth of [Mary will be thirty-five at s*] either; that proposition is expressed by (3). (In addition, (2) does not express the proposition that two months prior to s* Joseph was sure about the truth of [Mary will be thirty-five at some s** < s*].) In fact, (1) roughly expresses the proposition that two months prior to s* Joseph was sure about the truth of [Mary is currently thirty-five and will still be thirty-five at s*] (Smith (1978), Enc (1987)). Indeed, unlike (1), (1′) is usually quite odd (presumably because most speakers presuppose that, like them, Joseph can accept that Mary is thirty-five for a period of two – sometimes even twelve – months, but not that she is thirty-five for a period of twenty months). To explain why the embedded past in (2) “refers” to the embedded evaluation time, and why the embedded present in (1)/(1’) “refers” to a time much larger than that, we assume, with Abusch (1997), that these embedded tenses are indexical expressions governed by general constraints on ‘de re’ attitude reports, including – crucially – the Upper Limit Constraint. Expanding on Abusch (1997) and Percus (2013), we derive the Upper Limit Constraint itself from general principles as well.
(1) Two months ago, Joseph was sure that Mary is thirty-five. (2) Two months ago, Joseph was sure that Mary was thirty-five. (3) Two months ago, Joseph was sure that Mary would now be thirty-five. (1′) Twenty months ago, Joseph was sure that Mary is thirty-five.
- - - - Tuesday, Sep 10, 2019 - - - -
Computational Logic Seminar Tuesday, September 10, Time 2:00 - 4:00 PM
CUNY Graduate Center, Room 5382 Speaker: Sergei Artemov Title: Frame Theories: reasoning with possible worlds
A well-principled notion of epistemic theory as an axiomatic description of a given scenario in the possible worlds environment has been conspicuously absent in epistemic logic.
Given a verbal description of a situation, a typical epistemic user cherry-picks a “natural model” and regards it as a formalization of the original description thus ignoring the fact that there might be many different “natural models” of the same description.
We introduce theories in possible worlds (frame theories), establish their completeness, and offer as a foundational tool in epistemology.
- - - - Wednesday, Sep 11, 2019 - - - -
- - - - Thursday, Sep 12, 2019 - - - -
- - - - Friday, Sep 13, 2019 - - - -
Set Theory Seminar
CUNY Graduate Center, Room 6417
Friday, September 13, 10:00-11:45am
Gunter Fuchs, CUNY Simultaneous exact reflection and mutual stationarity
I will talk about a strengthening of a classical result of Foreman and Magidor, which states that any sequence of stationary subsets of distinct regular cardinals, each set consisting of ordinals of countable cofinality, is mutually stationary. The strengthening allows us to conclude a form of simultaneous reflection of stationarity which guarantees the existence of a mutually stationary sequence of exact reflection points, as a consequence of the subcomplete forcing axiom, and in fact of a weaker principle that corresponds to the subcomplete fragment of the well-known strong reflection principle.
Seminar in Logic, Games and Language
CUNY Graduate Center, Room 4421
Friday, September 13, 4:15-6:15
Ron Meyden, University of New South Wales TBA
Next Week in Logic at CUNY:
- - - - Monday, Sep 16, 2019 - - - -
Logic and Metaphysics Workshop Date: Monday, September 16th, 4.15-6.15 Place: Room 7314, CUNY Graduate Center Speaker: Ole Hjortland and Ben Martin (Bergen) Title: Anti-Exceptionalism and Explanations in Logic
Abstract: According to logical anti-exceptionalism we come to be justified in believing logical theories by similar means to scientific theories. This is often explained by saying that theory choice in logic proceeds via abductive arguments (Priest, Russell, Williamson, Hjortland). Thus, the success of classical and non-classical theories of validity are compared by their ability to explain the relevant data. However, as of yet there is no agreed upon account of which data logical theories must explain, and subsequently how they prove their mettle. In this paper, we provide a non-causal account of logical explanation, and show how it can accommodate important disputes about logic.
- - - - Tuesday, Sep 17, 2019 - - - -
- - - - Wednesday, Sep 18, 2019 - - - -
- - - - Thursday, Sep 19, 2019 - - - -
- - - - Friday, Sep 20, 2019 - - - -
Set Theory Seminar
CUNY Graduate Center, Room 6417
Friday, September 20, 10:00-11:45am
Sam Coskey, Boise State University TBA
Logic Workshop
CUNY Graduate Center, Room 6417
Friday, September 20, 2:00-3:30pm
Artem Chernikov, UCLA TBA
Seminar in Logic, Games and Language
CUNY Graduate Center, Room 4421
Friday, September 20, 4:15-6:15
Ignacio Ojea Quintana, Australian national University
TBA
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
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Logic Seminar NUS 12 September 2019 17:00 hrs
NUS Logic Seminar
9/9/2019
Invitation to the Logic Seminar at the National University of Singapore
Date: Thursday, 12 September 2019, 17:00 hrs
Room: S17#06-11, Department of Mathematics, NUS
Speaker: Gao Ziyuan
Title: The one-cop-moves game on planar graphs
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
Cops and Robbers is a vertex-pursuit game played on graphs. In
this game, a set of cops and a robber occupy the vertices of the graph
and move alternately along the graph's edges with perfect
information about each other' positions. If a cop
eventually occupies the same vertex as the robber, then the cops win;
the robber wins if she can indefinitely evade capture. Aigner and
Fromme established that in every connected planar graph, three cops
are sufficient to capture a single robber. In this paper, we consider
a recently studied variant of the cops and robbers game, alternately
called the one-active-cop game, one-cop-moves game or the lazy cops
and robbers game, where at most one cop can move during any round.
We show that Aigner and Fromme's result does not generalize to this game
variant by constructing a connected planar graph on which a robber can
indefinitely evade three cops in the one-cop-moves game.
This talk is based on joint work with Boting Yang
(http://www2.cs.uregina.ca/~boting/).
Tagged: Gao Ziyuan
This Week in Logic at CUNY
This Week in Logic at CUNY
9/8/2019
This Week in Logic at CUNY:
- - - - Monday, Sep 9, 2019 - - - -
Logic and Metaphysics Workshop Spring 2019 Date: Monday, September 9th, 4.15-6.15 Place: Room 7314, CUNY Graduate Center Speaker: Yael Sharvit (UCLA) Title: Temporal ‘de re’ Attitudes
Abstract: A sensible approach to the semantics of tense says that present tense and past tense “refer” to the evaluation time and to some pre-evaluation time, respectively. Indeed, this seems to be the case in unembedded sentences (e.g., Mary is thirty-five, Mary was thirty-five). But embedded tenses seem to misbehave: (1) does not express the proposition that two months prior to s* (= the speech time) Joseph was sure about the truth of [Mary is currently thirty-five]; this proposition is expressed by (2). Assuming that tenses are indexical expressions does not automatically solve the problem, since (1) does not express the proposition that two months prior to s* Joseph was sure about the truth of [Mary will be thirty-five at s*] either; that proposition is expressed by (3). (In addition, (2) does not express the proposition that two months prior to s* Joseph was sure about the truth of [Mary will be thirty-five at some s** < s*].) In fact, (1) roughly expresses the proposition that two months prior to s* Joseph was sure about the truth of [Mary is currently thirty-five and will still be thirty-five at s*] (Smith (1978), Enc (1987)). Indeed, unlike (1), (1′) is usually quite odd (presumably because most speakers presuppose that, like them, Joseph can accept that Mary is thirty-five for a period of two – sometimes even twelve – months, but not that she is thirty-five for a period of twenty months). To explain why the embedded past in (2) “refers” to the embedded evaluation time, and why the embedded present in (1)/(1’) “refers” to a time much larger than that, we assume, with Abusch (1997), that these embedded tenses are indexical expressions governed by general constraints on ‘de re’ attitude reports, including – crucially – the Upper Limit Constraint. Expanding on Abusch (1997) and Percus (2013), we derive the Upper Limit Constraint itself from general principles as well.
(1) Two months ago, Joseph was sure that Mary is thirty-five. (2) Two months ago, Joseph was sure that Mary was thirty-five. (3) Two months ago, Joseph was sure that Mary would now be thirty-five. (1′) Twenty months ago, Joseph was sure that Mary is thirty-five.
- - - - Tuesday, Sep 10, 2019 - - - -
- - - - Wednesday, Sep 11, 2019 - - - -
- - - - Thursday, Sep 12, 2019 - - - -
- - - - Friday, Sep 13, 2019 - - - -
Set Theory Seminar
CUNY Graduate Center, Room 6417
Friday, September 13, 10:00-11:45am
Gunter Fuchs, CUNY Simultaneous exact reflection and mutual stationarity
I will talk about a strengthening of a classical result of Foreman and Magidor, which states that any sequence of stationary subsets of distinct regular cardinals, each set consisting of ordinals of countable cofinality, is mutually stationary. The strengthening allows us to conclude a form of simultaneous reflection of stationarity which guarantees the existence of a mutually stationary sequence of exact reflection points, as a consequence of the subcomplete forcing axiom, and in fact of a weaker principle that corresponds to the subcomplete fragment of the well-known strong reflection principle.
Next Week in Logic at CUNY:
- - - - Monday, Sep 16, 2019 - - - -
Logic and Metaphysics Workshop Date: Monday, September 16th, 4.15-6.15 Place: Room 7314, CUNY Graduate Center Speaker: Ole Hjortland and Ben Martin (Bergen) Title: Anti-Exceptionalism and Explanations in Logic
Abstract: According to logical anti-exceptionalism we come to be justified in believing logical theories by similar means to scientific theories. This is often explained by saying that theory choice in logic proceeds via abductive arguments (Priest, Russell, Williamson, Hjortland). Thus, the success of classical and non-classical theories of validity are compared by their ability to explain the relevant data. However, as of yet there is no agreed upon account of which data logical theories must explain, and subsequently how they prove their mettle. In this paper, we provide a non-causal account of logical explanation, and show how it can accommodate important disputes about logic.
- - - - Tuesday, Sep 17, 2019 - - - -
- - - - Wednesday, Sep 18, 2019 - - - -
- - - - Thursday, Sep 19, 2019 - - - -
- - - - Friday, Sep 20, 2019 - - - -
Set Theory Seminar
CUNY Graduate Center, Room 6417
Friday, September 20, 10:00-11:45am
Sam Coskey, Boise State University TBA
Logic Workshop
CUNY Graduate Center, Room 6417
Friday, September 20, 2:00-3:30pm
Artem Chernikov, UCLA TBA
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
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If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
UPDATE: This Week in Logic at CUNY
This Week in Logic at CUNY
9/2/2019
Hi everyone,
Please note the addition of the Computational Logic Seminar, meeting tomorrow (Tuesday).
Best,
Jonas
This Week in Logic at CUNY:
- - - - Monday, Sep 2, 2019 - - - -
- - - - Tuesday, Sep 3, 2019 - - - -
Computational Logic Seminar Fall Semester 2019 Time 2:00 - 4:00 PM, Tuesday, September 3 CUNY Graduate Center, Room 5382 Speaker: Sergei Artemov Title: Justification Awareness Models and modeling Russell/Gettier phenomenon.
How to model awareness and respect epistemic closure. Justification view of Kripke semantics. New research directions.
- - - - Wednesday, Sep 04, 2019 - - - -
- - - - Thursday, Sep 05, 2019 - - - -
- - - - Friday, Sep 06, 2019 - - - -
Logic Workshop CUNY Graduate Center, Room 6417 Friday, September 6, 2:00-3:30pm
Russell Miller, CUNY
A computability-theoretic proof of Lusin's Theorem
Lusin's Theorem, from real analysis, states that for every Borel-measurable function ff from RR to RR, and for every ϵ>0ϵ>0, there exists a continuous function gg on RR such that {x∈R:f(x)≠g(x)}{x∈R : f(x)≠g(x)}has measure <ϵ<ϵ. This is proven in most introductory real analysis courses, but here we will give a proof using computability theory and computable analysis. In addition to the theorem itself, the proof will establish an effective way of producing gg from ff and ϵϵ, and will pick out, for each ff, the specific set of troublemakers xx in RR that create all the discontinuities.
Seminar in Logic, Games and Language CUNY Graduate Center, Room 4421 Friday, September 6, 4:15-6:15
Our next meeting will be on September 6 and we will go over Christian List's survey article on Social Choice from the Stanford Encyclopedia of Philosophy.
Logic and Metaphysics Workshop Spring 2019 Date: Monday, September 9th, 4.15-6.15 Place: Room 7314, CUNY Graduate Center Speaker: Yael Sharvit (UCLA) Title: Temporal ‘de re’ Attitudes
Abstract: A sensible approach to the semantics of tense says that present tense and past tense “refer” to the evaluation time and to some pre-evaluation time, respectively. Indeed, this seems to be the case in unembedded sentences (e.g., Mary is thirty-five, Mary was thirty-five). But embedded tenses seem to misbehave: (1) does not express the proposition that two months prior to s* (= the speech time) Joseph was sure about the truth of [Mary is currently thirty-five]; this proposition is expressed by (2). Assuming that tenses are indexical expressions does not automatically solve the problem, since (1) does not express the proposition that two months prior to s* Joseph was sure about the truth of [Mary will be thirty-five at s*] either; that proposition is expressed by (3). (In addition, (2) does not express the proposition that two months prior to s* Joseph was sure about the truth of [Mary will be thirty-five at some s** < s*].) In fact, (1) roughly expresses the proposition that two months prior to s* Joseph was sure about the truth of [Mary is currently thirty-five and will still be thirty-five at s*] (Smith (1978), Enc (1987)). Indeed, unlike (1), (1′) is usually quite odd (presumably because most speakers presuppose that, like them, Joseph can accept that Mary is thirty-five for a period of two – sometimes even twelve – months, but not that she is thirty-five for a period of twenty months). To explain why the embedded past in (2) “refers” to the embedded evaluation time, and why the embedded present in (1)/(1’) “refers” to a time much larger than that, we assume, with Abusch (1997), that these embedded tenses are indexical expressions governed by general constraints on ‘de re’ attitude reports, including – crucially – the Upper Limit Constraint. Expanding on Abusch (1997) and Percus (2013), we derive the Upper Limit Constraint itself from general principles as well.
(1) Two months ago, Joseph was sure that Mary is thirty-five. (2) Two months ago, Joseph was sure that Mary was thirty-five. (3) Two months ago, Joseph was sure that Mary would now be thirty-five. (1′) Twenty months ago, Joseph was sure that Mary is thirty-five.
- - - - Tuesday, Sep 10, 2019 - - - -
- - - - Wednesday, Sep 11, 2019 - - - -
- - - - Thursday, Sep 12, 2019 - - - -
- - - - Friday, Sep 13, 2019 - - - -
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
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Wednesday seminar
Prague Set Theory Seminar
9/2/2019
Dear all,
The seminar meets on Wednesday September 4th at 11:00 in the Institute
of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: David Uhrik -- Forcing axioms and rectangular partition relations
We will discus the consistency of certain rectangular partition
relations and the existence of a Suslin tree.
Best,
David
Tagged: David Uhrik
This Week in Logic at CUNY
This Week in Logic at CUNY
9/1/2019
This Week in Logic at CUNY:
- - - - Monday, Sep 2, 2019 - - - -
- - - - Tuesday, Sep 3, 2019 - - - -
- - - - Wednesday, Sep 04, 2019 - - - -
- - - - Thursday, Sep 05, 2019 - - - -
- - - - Friday, Sep 06, 2019 - - - -
Logic Workshop CUNY Graduate Center, Room 6417 Friday, September 6, 2:00-3:30pm
Russell Miller, CUNY
A computability-theoretic proof of Lusin's Theorem
Lusin's Theorem, from real analysis, states that for every Borel-measurable function ff from RR to RR, and for every ϵ>0ϵ>0, there exists a continuous function gg on RR such that {x∈R:f(x)≠g(x)}{x∈R : f(x)≠g(x)}has measure <ϵ<ϵ. This is proven in most introductory real analysis courses, but here we will give a proof using computability theory and computable analysis. In addition to the theorem itself, the proof will establish an effective way of producing gg from ff and ϵϵ, and will pick out, for each ff, the specific set of troublemakers xx in RR that create all the discontinuities.
Seminar in Logic, Games and Language CUNY Graduate Center, Room 4421 Friday, September 6, 4:15-6:15
Our next meeting will be on September 6 and we will go over Christian List's survey article on Social Choice from the Stanford Encyclopedia of Philosophy.
Logic and Metaphysics Workshop Spring 2019 Date: Monday, September 9th, 4.15-6.15 Place: Room 7314, CUNY Graduate Center Speaker: Yael Sharvit (UCLA) Title: Temporal ‘de re’ Attitudes
Abstract: A sensible approach to the semantics of tense says that present tense and past tense “refer” to the evaluation time and to some pre-evaluation time, respectively. Indeed, this seems to be the case in unembedded sentences (e.g., Mary is thirty-five, Mary was thirty-five). But embedded tenses seem to misbehave: (1) does not express the proposition that two months prior to s* (= the speech time) Joseph was sure about the truth of [Mary is currently thirty-five]; this proposition is expressed by (2). Assuming that tenses are indexical expressions does not automatically solve the problem, since (1) does not express the proposition that two months prior to s* Joseph was sure about the truth of [Mary will be thirty-five at s*] either; that proposition is expressed by (3). (In addition, (2) does not express the proposition that two months prior to s* Joseph was sure about the truth of [Mary will be thirty-five at some s** < s*].) In fact, (1) roughly expresses the proposition that two months prior to s* Joseph was sure about the truth of [Mary is currently thirty-five and will still be thirty-five at s*] (Smith (1978), Enc (1987)). Indeed, unlike (1), (1′) is usually quite odd (presumably because most speakers presuppose that, like them, Joseph can accept that Mary is thirty-five for a period of two – sometimes even twelve – months, but not that she is thirty-five for a period of twenty months). To explain why the embedded past in (2) “refers” to the embedded evaluation time, and why the embedded present in (1)/(1’) “refers” to a time much larger than that, we assume, with Abusch (1997), that these embedded tenses are indexical expressions governed by general constraints on ‘de re’ attitude reports, including – crucially – the Upper Limit Constraint. Expanding on Abusch (1997) and Percus (2013), we derive the Upper Limit Constraint itself from general principles as well.
(1) Two months ago, Joseph was sure that Mary is thirty-five. (2) Two months ago, Joseph was sure that Mary was thirty-five. (3) Two months ago, Joseph was sure that Mary would now be thirty-five. (1′) Twenty months ago, Joseph was sure that Mary is thirty-five.
- - - - Tuesday, Sep 10, 2019 - - - -
- - - - Wednesday, Sep 11, 2019 - - - -
- - - - Thursday, Sep 12, 2019 - - - -
- - - - Friday, Sep 13, 2019 - - - -
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io (site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
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If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Logic Seminar 5 Sept 2019 17:00 hrs at NUS
NUS Logic Seminar
8/30/2019
Invitation to the Logic Seminar at the National University of Singapore
Date: Thursday, 5 September 2019, 17:00 hrs
Room: S17#06-11, Department of Mathematics, NUS
Speaker: Samuel Alfaro Tanuwijaya
Title: Pseudo-finite fields
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: This talk will introduce pseudofinite fields and how they are
axiomatized. We will see how they are infinite models of the theory of finite
fields, and therefore there is no theory whose models are exactly the finite
fields.
Tagged: Samuel Alfaro Tanuwijaya
Logic Seminar
Barcelona Logic Seminar
8/28/2019 5:08:29
Next session of the Logic Seminar
Tomás Ibarlucía (Institut de Mathématiques de Jussieu-Paris Rive
Gauche, Université Paris Diderot )
PROPERTY (T) FOR AUTOMORPHISM GROUPS OF SEPARABLY CATEGORICAL STRUCTURES
Wednesday, September 4.
12:30
IMUB Lecture Room, Facultat de Matemàtiques i Informàtica, UB.
http://www.ub.edu/slb/Seminar.html
Aquest missatge, i els fitxers adjunts que hi pugui haver, pot contenir informació confidencial o protegida legalment i s’adreça exclusivament a la persona o entitat destinatària. Si no consteu com a destinatari final o no teniu l’encàrrec de rebre’l, no esteu autoritzat a llegir-lo, retenir-lo, modificar-lo, distribuir-lo, copiar-lo ni a revelar-ne el contingut. Si l’heu rebut per error, informeu-ne el remitent i elimineu del sistema tant el missatge com els fitxers adjunts que hi pugui haver.
Este mensaje, y los ficheros adjuntos que pueda incluir, puede contener información confidencial o legalmente protegida y está exclusivamente dirigido a la persona o entidad destinataria. Si usted no consta como destinatario final ni es la persona encargada de recibirlo, no está autorizado a leerlo, retenerlo, modificarlo, distribuirlo o copiarlo, ni a revelar su contenido. Si lo ha recibido por error, informe de ello al remitente y elimine del sistema tanto el mensaje como los ficheros adjuntos que pueda contener.
This email message and any attachments it carries may contain confidential or legally protected material and are intended solely for the individual or organization to whom they are addressed. If you are not the intended recipient of this message or the person responsible for processing it, then you are not authorized to read, save, modify, send, copy or disclose any part of it. If you have received the message by mistake, please inform the sender of this and eliminate the message and any attachments it carries from your account.
Logic Seminar 29 Aug 2019 17:00 hrs at NUS S17#06-11
NUS Logic Seminar
8/22/2019
Invitation to the Logic Seminar at the National University of Singapore
Date: Thursday, 29 August 2019, 17:00 hrs
Room: S17#06-11, Department of Mathematics, NUS
Speaker: Chong Chi Tat
Title: Revisiting Seetapun's theorem with his disjunction
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: Ramsey's theorem RT^n_2 states that if the
n-rtuples of the set of natural numbers are coloured in either red or
blue, then there is an infinite subset all of whose n-tuples have the
same color. The proof-theoretic strength of RT^n_2 has been a
prominent line of study in reverse mathematics. The first major
breakthrough was obtained by David Seetapun (Seetapun and Slaman
(1995)) who showed that RT^2_2 is strictly weaker than RT^3_2. This
talk will describe a proof of this theorem using the technique called
"Seetapun disjunction" introduced in Chong, Slaman and Yang (2014).
Tagged: Chong Chi Tat
Wednesday seminar
Prague Set Theory Seminar
8/22/2019
Dear all,
There will be no seminar next week, the seminar should meet again on
Wednesday September 4th.
Best,
David
Haim Horowitz: Recent progress in the study of the definability of mad families
Toronto Set Theory Seminar
8/21/2019
Place: Fields Institute (Room 210)
Date: 23 August, 2019 (13:30-15:00)
Speaker: Haim Horowitz
Title: Recent progress in the study of the definability of mad families
Abstract:
I'll review some of the recent progress and the many open problems in the
study of the definability of mad families. Among the new results are
connections to Ramsey theory, Baire class one functions and generalized
descriptive set theory. Additionally, I'll indicate how some techniques
originating in the study of the definability of mad families provide
solutions to open problems in other areas, such as choiceless set theory
and the study of ultrafilters in L(R)[U]. The contents of the talk will be
almost disjoint to the contents of Törnquist's talk from May.
Tagged: Haim Horowitz
Eva Pernecká : A notion of support in Lipschitz-free spaces
IMPAN Working Group in Applications of Set Theory
8/20/2019
Seminar: Working group in applications of set theory, IMPAN
Thursday, 22.09.2019, 10:15, room 105, IMPAN
Speaker: Eva Pernecká (Czech Technical University in Prague),
Title: "A notion of support in Lipschitz-free spaces"
Abstact: "We will show that the class of free spaces over closed subspaces of a complete metric space is closed under arbitrary intersections and that this leads to a natural definition of support applicable to all elements of free spaces. Although this property does not seem surprising, the proof is rather nontrivial. It follows from the particular algebraic structure of the spaces of Lipschitz functions (the isometric dual of the free space) described by Weaver. We will discuss some characterizations and properties of supports. We will present their application to the study of extreme points of free spaces. And finally, we will have a look at the elements of free spaces induced by Radon measures. This is a joint work with Ramón J. Aliaga".
Visit our seminar page which may include some future talks at https://www.impan.pl/~set_theory/Seminar/
Tagged: Eva Pernecká
Saeed Ghasemi: Universal AF-algebras
IMPAN Working Group in Applications of Set Theory
8/19/2019
Seminar: Working group in applications of set theory, IMPAN
Tuesday, 20.08.2019, 14.00, ******ROOM 403******, IMPAN
Speaker: Saeed Ghasemi (Czech Academy of Sciences),
Title: "Universal AF-algebras"
Abstact: "We study the approximately finite-dimensional (AF) C*-algebras that appear as inductive limits of sequences of finite-dimensional C*-algebras and left-invertible embeddings. We show that there is such a separable AF-algebra that satisfies similar homogeneity and universality properties as the Cantor set. Joint work with Wiesław Kubiś, see: arxiv.org/pdf/1903.10392.pdf"
Visit our seminar page which may include some future talks (perhaps even three until October) at https://www.impan.pl/~set_theory/Seminar/
Tagged: Saeed Ghasemi
Logic workshop in Nanjing, May 11-30, 2020
Conference
8/16/2019
The 3-week long workshop is intended to bring mathematical logicians together to work intensively. This is nothing like a conference. Talks will be arranged occasionally each week during the workshop. The participants are expected to have some specific topics to work together about one or two weeks. We will fully cover accommodations of participants. Other people who can get support from other sources are also welcome. This year the topic will be focused on applied model theory, interactions between set theory and recursion theory.
Logic Seminar 22 Aug 2019 17:00 hrs @ NUS S17#06-11
NUS Logic Seminar
8/15/2019
Invitation to the Logic Seminar at the National University of Singapore
Date: Thursday, 22 August 2019, 17:00 hrs
Room: S17#06-11, Department of Mathematics, NUS
Speaker: Johanna Franklin
Title: Degrees of isometric isomorphism for Banach spaces
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: The degree of isomorphism of a computable presentation of a
structure is the least powerful Turing degree that computes an isomorphism
from this presentation onto the "standard" copy of the structure, assuming
that such a copy exists. I will discuss the degrees of isometric
isomorphism of two of the five types of nonzero separable L^p spaces and
then consider lowness for isometric isomorphism for these spaces. Time
permitting, I will discuss lowness for isometric isomorphism and lowness
for isometry in a more general context.
Joint work with Tim McNicholl
Tagged: Johanna Franklin
Wednesday seminar
Prague Set Theory Seminar
8/14/2019
Dear all,
The seminar meets on Wednesday August 21st at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Osvaldo Guzman -- On weakly universal functions
A function U: [ω_1]^2 -> 2 is called universal if for every function F:
[ω_1]^2 -> ω there is an injective function h: ω_1 -> ω_1 such that
F(α,β) =U(h(α), h(β)) for each α,β ∈ ω_1. It is easy to see that
universal functions exist assuming the Continuum Hypothesis,
furthermore, by results of Shelah and Mekler, the existence of such
functions is consistent with the continuum being arbitrarily large.
Universal functions were recently studied by Shelah and Steprāns, they
showed that the existence of universal graphs is consistent with several
values of the dominating and unbounded numbers. They also considered
several variations of universal functions, in particular, the following
notion was studied: A function U: [ω_1]^2 -> ω is (1,ω_1)-weakly
universal if for every F: [ω_1]^2 -> ω there is an injective function h:
ω_1 -> ω_1 and a function e: ω -> ω such that F(α,β) = e(U(h(α), h(β)))
for every α,β ∈ ω_1. Shelah and Steprāns asked if (1,ω_1)-weakly
universals functions exist in ZFC. We will study the existence of
(1,ω_1)-weakly universal functions in Sacks models and provide an answer
to their problem.
Best,
David
Rutgers MAMLS, November 1-3, 2019
Conference
8/12/2019
Rutgers MAMLS 2019
November 1-3
Department of Mathematics, Rutgers University
Conference home page
Speakers:
Sandra Mueller
Christian Rosendal
Justin Moore
Saharon Shelah
James Freitag
Assaf Shani
Steve Jackson
Pierre Simon
John Steel
Chris Laskowski
While graduate students, young researchers, female mathematicians and members of under-represented groups are particularly encouraged to apply for travel support, it should be stressed that any participants without their own sources of funding are eligible to apply. Requests will be handled on a case-by-case basis within the limits of the budget. Please send an email to Russell.Miller@qc.cuny.edu
Tagged: Sandra Mueller, Christian Rosendal, Justin Moore, Saharon Shelah, James Freitag, Assaf Shani, Steve Jackson, Pierre Simon, John Steel, Chris Laskowski
Wednesday seminar
Prague Set Theory Seminar
8/1/2019
Dear all,
There will be no Wednesday seminar during the next two weeks. You might
be interesting in the following conferences instead:
http://clmpst2019.flu.cas.cz/
https://lc2019.cz/
The seminar should meet again on Wednesday August 21st for a talk by
Osvaldo Guzman.
Best,
David
No set theory seminar this week
Toronto Set Theory Seminar
7/26/2019
Hi everyone,
We will not have a seminar on July 26.
If you would like t give a talk in the near future, please let me know.
Best regards,
Osvaldo Guzman
Ziemowit Kostana: On countably saturated linear orders and graphs
Prague Set Theory Seminar
7/24/2019
Dear all,
The seminar meets on Wednesday July 31st at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Ziemowit Kostana -- On countably saturated linear orders and graphs
Abstract attached
Participants of the seminar might be also interested in the Midsummer
Combinatorial Workshop which will take place at Mala Strana during the
next week.
https://kam.mff.cuni.cz/workshops/mcw/
Best,
David
Tagged: Ziemowit Kostana
Jindřich Zapletal: Chromatic numbers of locally countable
hypergraphs
Prague Set Theory Seminar
7/19/2019
Dear all,
The seminar meets on Wednesday July 24th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Jindřich Zapletal -- Chromatic numbers of locally countable
hypergraphs
I will introduce several variants of chromatic numbers of Borel locally
countable hypergraphs and show how they can be separated in choiceless
set theory.
Best,
David
Tagged: Jindřich Zapletal
No set theory seminar this week
Toronto Set Theory Seminar
7/19/2019
Hi everyone,
There will not be a set theory seminar on
19 July.
If someone would like to give a talk in the near future,
please let me know.
Osvald Guzman
Logic Seminar Talk at NUS today
NUS Logic Seminar
7/15/2019
Invitation to the Logic Seminar at the National University of Singapore
Date: Tuesday, 16 July 2019, 16:00 hrs
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Andre Nies
Title: Random sequences of quantum bits
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
Martin-Loef formalised in 1966 the intuitive notion of randomness
of infinite sequences of bits via algorithmic tests. In this talk,
we investigate what happens if we replace classical bits by
quantum bits.
We first provide a framework to formalise infinite sequences
of quantum bits as states of a suitable C* algebra.
Thereafter we introduce an analog of Martin-Loef's notion. We show
that for classical bit sequences the two notions coincide. We also
discuss quantum Kolmogorov complexity for finite sequences of quantum
bits and its relationship to quantum Martin-Loef randomness. Finally,
we consider an effective version of the Shannan-McMillan-Breiman theorem
in the quantum setting.
This is joint work with Volkher Scholz. The paper is available at
http://arxiv.org/abs/1709.08422.
Tagged: Andre Nies
Viera Šottová: Ideals on natural numbers and combinatorial
characterization of sigma-ideal N
Prague Set Theory Seminar
7/11/2019
Dear all,
The seminar meets on Wednesday July 17th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Viera Šottová -- Ideals on natural numbers and combinatorial
characterization of sigma-ideal N
Historically, there is a lot of interesting results about Cichoń's
diagram as well as corresponded objects. Particularly, Bartoszyński
adduced several nice combinatorial characterizations of notions which we
are interested in.
We mainly study an ideal of Lebesgue measure zero sets, denoted N and we
briefly modify its characterization with respect to ideals on natural
numbers. We obtain a family N_J which is sigma-ideal as well.
Additionally, it is a subset of N. On the other hand, N_J expresses a
connection between ideals on natural numbers and ideals on real line. We
deal with common cardinal invariants of such families and their relation
to original notion.
Joint work with D. A. Mejia
Best,
David
Tagged: Viera Šottová
Michael Hrušák: Countably compact groups without convergent
sequences
Prague Set Theory Seminar
7/4/2019
Dear all,
The seminar meets on Wednesday July 10th.
THERE IS A TIME CHANGE, WE WILL MEET AT 12:00 (instead of 11) in the
Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front
building.
Program: Michael Hrušák -- Countably compact groups without convergent
sequences
In a joint work with J. van Mill, U.A. Ramos Garcia and S. Shelah we
solve a longstanding problem of E. van Douwen by constructing, in ZFC, a
countably compact topological group without non-trivial convergent
sequences.
Best,
David
Tagged: Michael Hrušák
Maxim Burke: Comonotone approximation and interpolation by entire functions
Toronto Set Theory Seminar
7/2/2019
Place: Fields Institute (Room 210)
Date: July 5, 2019 (13:30-15:00)
Speaker: Maxim Burke
Title: Comonotone approximation and interpolation by entire functions
Abstract: We discuss some theorems on approximation of a real function f
whose derivatives up to order n are piecewise monotone by an entire
function g whose derivatives up to order n are comonotone with those of f
(increasing and decreasing on the same intervals) with interpolation on a
closed discrete set. One of the theorems depends on a conjecture regarding
the nature of the set of (n+1)-tuples (f(1),f'(1),f''(1),...) of final
values of C^n functions f on [0,1] whose derivatives at the origin are zero
and whose nth derivative is increasing but not constant. The work has its
origins in the problem of finding entire order-isomorphisms of everywhere
nonmeager subsets of R.
Tagged: Maxim Burke
No set theory seminar this week
Toronto Set Theory Seminar
6/27/2019
Hi everyone, there will not be a set theoryseminar this week.
Osvaldo Guzman
Clovis Hamel: Definability, Topology of Function Spaces, and Continuous Logics.
Toronto Set Theory Seminar
6/21/2019
Place: Fields Institute (Room 210)
Date: 21 June, 2019 (13:00-13:50)
Speaker: Clovis Hamel
Title: Definability, Topology of Function Spaces, and Continuous Logics.
Abstract: In first-order logic, the notion of stability has been a driving
force of Model Theory in the last decades since Shelah introduced it. A
most relevant connection occurs in first-order logic: stability and
definability are equivalent. The classical definition of stability
involves the computation of cardinalities of spaces of types. However,
there are several equivalent definitions, most notably “no formula has the
order property”. We will present another approach to stability using
double limit conditions which is more suitable for continuous logics.
Using results from C${}_{p}$-theory, , i.e. the topology of real-valued
function spaces, we will show connections among double limit conditions,
stability and definability in various continuous logics. As an
application, we will expand some work of Casazza and Iovino concerning
Gower’s problem on the definability of pathological Banach spaces not
including isomorphic copies of $l^p$ or $c_0$ in compact logics to
stablish similar undefinability results for (continuous)
${\mathcal{L}}_{{\omega }_1,\omega }$. We will also discuss further lines
on research in this direction.
Tagged: Clovis Hamel
Wednesday seminar
Prague Set Theory Seminar
6/19/2019
Dear all,
There will be no seminars during the next two weeks (most of the regular
participants are away).
The seminar should meet again on Wednesday July 10th for a talk by
Michael Hrušák.
Best,
David
Wednesday seminar
Prague Set Theory Seminar
6/13/2019
Dear all,
The seminar meets on Wednesday June 19th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Jindřich Zapletal -- Matroids and the Axiom of Choice
Abstract: I will produce a model of ZF+DC with a Hamel basis or
transcendence basis for the reals over the rationals in an optimal way.
The two tasks are completely different, reflecting the model theoretic
distinctions between vectors spaces and fields. I will spend some time
outlining the basics of matroid theory, which is highly relevant for
this problem.
Best,
David
Tagged: Jindřich Zapletal
Piotr Szewczak: Products of gamma-sets
Toronto Set Theory Seminar
6/13/2019
Place: Fields Institute (Room 210)
Date: 14 June, 2019 (13:30-15:00)
Speaker:Piotr Szewczak
Title: Products of gamma-sets
Abstract: Let X be a set of reals and Cp(X) be the set of all continuous
real-valued functions on X with the pointwise convergence topology. By the
result of Gerlits and Nagy the space Cp(X) has the Frechet-Urysohn
property (a generalization of first-countability) if and only if the set X
is a gamma-set (i.e., has a combinatorial covering property). The
existence of uncountable gamma-sets of reals is independent of ZFC. Tsaban
proved that sets with some special combinatorial structure are gamma-sets.
We generalize this class of sets and prove that their products have the
property gamma. We also show that for every set X from our class and every
gamma set Y, the product space X x Y have a strong property weaker than
gamma. These investigations are motivated by the result of Miller, Tsaban
and Zdomskyy that under CH,
there are two gamma-sets whose product space is not even Menger (in
particular it is not gamma). This is a joint work with Magdalena Włudecka.
Tagged: Piotr Szewczak
Piotr Koszmider; Lifting uncountable combinatorics to the Banach space level: Banach spaces C(K) with few operators. Part 4.
IMPAN Working Group in Applications of Set Theory
6/9/2019
Seminar: Working group in applications of set theory, IMPAN
Thursday, 13.06.2019, 10:15, room 105, IMPAN
Speaker: Piotr Koszmider (IMPAN)
Title: "Lifting uncountable combinatorics to the Banach space level: Banach spaces C(K) with few operators. Part 4."
Abstact: "This series of 4 talks will be a minicourse on Banach spaces of continuous functions which have few operators, projections, injections etc. In particular they can be indecomposable and nonisomorphic with their hyperplanes. To obtain this linear operator level rigidity one needs to construct compact Ks which are not only rigid in the usual sense, i.e., in terms of continuous mappings on K. One needs to deal with weak* continuous functions from K into the space M(K) of Radon measures on K, so the combinatorics of the constructions needs stronger conditions than for endo-rigid Boolean algebras or strongly rigid compact spaces. We will present main arguments leading to C(K)s with the required properties but the proofs of many lemmas will be omitted. The talks should be accessible to everyone with general analytic and topological background".
This is the last regular meeting of the seminar this academic year. We may have some extraordinary meetings during the summer which will be announced here.
Visit our seminar page which may include some future talks at https://www.impan.pl/~set_theory/Seminar/
Tagged: Piotr Koszmider
No seminar this week
Toronto Set Theory Seminar
6/6/2019
Hi everyone!
We will not have a seminar this week.
If you are iterested in giving a talk in the
near future, please let me know.
Osvaldo Guzman
Wednesday seminar
Prague Set Theory Seminar
6/6/2019
Dear all,
The seminar meets on Wednesday June 12th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
There is no fixed programme yet, walk in speakers are welcome.
The backup option is me talking about something, probably results of A.
Dow on P-points in the random model.
Best,
David
Piotr Koszmider; Lifting uncountable combinatorics to the Banach space level: Banach spaces C(K) with few operators. Part 3.
IMPAN Working Group in Applications of Set Theory
6/2/2019
Seminar: Working group in applications of set theory, IMPAN
NOTE: WE ARE BACK IN THE USUAL ROOM
Thursday, 06.06.2019, 10:15, room 105, IMPAN
Speaker: Piotr Koszmider (IMPAN)
Title: "Lifting uncountable combinatorics to the Banach space level: Banach spaces C(K) with few operators. Part 3."
Abstact: "This series of 4 talks will be a minicourse on Banach spaces of continuous functions which have few operators, projections, injections etc. In particular they can be indecomposable and nonisomorphic with their hyperplanes. To obtain this linear operator level rigidity one needs to construct compact Ks which are not only rigid in the usual sense, i.e., in terms of continuous mappings on K. One needs to deal with weak* continuous functions from K into the space M(K) of Radon measures on K, so the combinatorics of the constructions needs stronger conditions than for endo-rigid Boolean algebras or strongly rigid compact spaces. We will present main arguments leading to C(K)s with the required properties but the proofs of many lemmas will be omitted. The talks should be accessible to everyone with general analytic and topological background.".
Visit our seminar page which may include some future talks at https://www.impan.pl/~set_theory/Seminar/
Tagged: Piotr Koszmider
Wednesday seminar
Prague Set Theory Seminar
5/31/2019
Dear all,
The seminar meets on Wednesday June 5th at 11:00.
*** CHANGE OF LOCATION ***
Due to a scheduled interruption to the water supply in Zitna the seminar
will meet next week at an alternative location: room 119 (next to the
Department of Logic office), Faculty of Arts, Charles University,
Celetná 20, Praha 1.
Program: Šárka Stejskalová -- Stationary reflection and its variants
Abstract: If κ is a regular cardinal and S is a stationary subset of κ,
we say that S reflects at α of uncountable cofinality if S∩α is "large"
in a certain sense (for instance stationary or containing a club). We
will discuss several forms of stationary reflection and review an
argument for adding a club to ω2 which is contained in a stationary set
S concentrated on ordinals with countable cofinality plus all ordinals
of uncountable cofinality. This is for instance used by Harrington and
Shelah to show that from a Mahlo cardinal one can get a model where
every stationary subset of ω2 which concentrates on ordinal with
countable cofinality reflects at some α<ω2 with cofinality ω1 (i.e. S∩α
is stationary). We will indicate some original results in this direction.
Best,
David
Tagged: Šárka Stejskalová
Dilip Raghavan: Order dimension of locally countable partial orders.
Toronto Set Theory Seminar
5/30/2019
Place: Fields Institute (Room 210)
Date: 31 May, 2019 (13:30-15:00)
Speaker: Dilip Raghavan
Title: Order dimension of locally countable partial orders
Abstract: I will present some recent results on order dimension, focusing
in the locally finite and locally countable orders. This is joint work
with several people.
Tagged: Dilip Raghavan
(KGRC) talk in the research seminar NEXT week, June 6
Kurt Godel Research Center
5/29/2019
The KGRC welcomes Neil Barton, Boaz Tsaban, Leandro Aurichi and Assaf
Shani as guests. Dr. Barton (host: Sy-David Friedman) will stay from June
3 to June 9. Professor Tsaban (host: Lyubomyr Zdomskyy) will stay from
June 16 to July 5 and give a talk for the European Set Theory Conference.
Professor Aurichi (host: Lyubomyr Zdomskyy) will stay from June 17 to July
3. Mr. Shani will stay from June 23 to July 31.
* * *
Please note that there will be no talk in the research seminar tomorrow,
May 30 (Ascension Day).
* * *
Research seminar
Kurt Göel Research Center
Thursday, June 6
"On convergent sequences of normalised measures on compact spaces"
Damian Sobota (KGRC)
The celebrated Josefson--Nissenzweig theorem---in a special case of a
Banach space $C(K)$ of continuous real-valued functions on an infinite
compact Hausdorff space $K$---asserts that there exists a sequence of
Radon measures $(\mu_n)$ on $K$ such that the total-variation of each
$\mu_n$ is $1$ and for every continuous function $f\in C(K)$ the sequence
of the integrals $\int_Kfd\mu_n$ converges to $0$. All the recent natural
proofs of the theorem start more or less as follows: "Assume there is not
such a sequence $(\mu_n)$ but with an additional property that each
$\mu_n$ is a finite linear combination of one-point measures (Dirac's
deltas). Then, ..." Although the proofs are correct, it appears that it is
not clear at all when this assumption is satisfied. During my talk I will
show when (and when not) it is the case that a compact space $K$ admits a
such a sequence of measures. As examples Efimov spaces, products of
compact spaces, Stone spaces of some funny Boolean algebras will appear.
This is a joint work with Lyubomyr Zdomskyy.
Time and Place
Tea at 3:30pm in the KGRC meeting room
Talk at 4:00pm in the KGRC lecture room
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de recibirlo, no está autorizado a leerlo, retenerlo, modificarlo, distribuirlo o copiarlo, ni a revelar su contenido. Si lo ha recibido por error, informe de ello al remitente y elimine del sistema tanto el mensaje como los ficheros adjuntos que pueda contener.
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from your account.
Piotr Koszmider; Lifting uncountable combinatorics to the Banach space level: Banach spaces C(K) with few operators. Part 2.
IMPAN Working Group in Applications of Set Theory
5/26/2019
Seminar: Working group in applications of set theory, IMPAN
NOTE CHANGE OF THE ROOM
Thursday, 30.05.2019, 10:15, ******ROOM 408******, IMPAN
Speaker: Piotr Koszmider (IMPAN)
Title: "Lifting uncountable combinatorics to the Banach space level: Banach spaces C(K) with few operators. Part 2."
Abstact: "This series of 4 talks will be a minicourse on Banach spaces of continuous functions which have few operators, projections, injections etc. In particular they can be indecomposable and nonisomorphic with their hyperplanes. To obtain this linear operator level rigidity one needs to construct compact Ks which are not only rigid in the usual sense, i.e., in terms of continuous mappings on K. One needs to deal with weak* continuous functions from K into the space M(K) of Radon measures on K, so the combinatorics of the constructions needs stronger conditions than for endo-rigid Boolean algebras or strongly rigid compact spaces. We will present main arguments leading to C(K)s with the required properties but the proofs of many lemmas will be omitted. The talks should be accessible to everyone with general analytic and topological background.".
Visit our seminar page which may include some future talks at https://www.impan.pl/~set_theory/Seminar/
Tagged: Piotr Koszmider
Wednesday seminar
Prague Set Theory Seminar
5/23/2019
Dear all,
The seminar meets on Wednesday May 29th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
There is no fixed program yet, the backup option is me presenting
results of Raghavan on PID and weak squares.
Best,
David
Logic Seminar
Barcelona Logic Seminar
5/22/2019 13:12:28
Next session of the Logic Seminar
Kameryn Williams (Department of Mathematics, University of Hawai'i at Mānoa)
THE COMPUTABLE STRUCTURE OF FORCING
Wednesday, May 29.
12:00
IMUB Lecture Room, Facultat de Matemàtiques i Informàtica, UB.
Aquest missatge, i els fitxers adjunts que hi pugui haver, pot contenir informació confidencial o protegida legalment i s’adreça exclusivament a la persona o entitat destinatària. Si no consteu com a destinatari final
o no teniu l’encàrrec de rebre’l, no esteu autoritzat a llegir-lo, retenir-lo, modificar-lo, distribuir-lo, copiar-lo ni a revelar-ne el contingut. Si l’heu rebut per error, informeu-ne el remitent i elimineu del sistema tant el missatge com els fitxers adjunts
que hi pugui haver.
Este mensaje, y los ficheros adjuntos que pueda incluir, puede contener información confidencial o legalmente protegida y está exclusivamente dirigido a la persona o entidad destinataria. Si usted no consta como destinatario final ni es la persona encargada
de recibirlo, no está autorizado a leerlo, retenerlo, modificarlo, distribuirlo o copiarlo, ni a revelar su contenido. Si lo ha recibido por error, informe de ello al remitente y elimine del sistema tanto el mensaje como los ficheros adjuntos que pueda contener.
This email message and any attachments it carries may contain confidential or legally protected material and are intended solely for the individual or organization to whom they are addressed. If you are not the intended recipient of this message or the person
responsible for processing it, then you are not authorized to read, save, modify, send, copy or disclose any part of it. If you have received the message by mistake, please inform the sender of this and eliminate the message and any attachments it carries
from your account.
Asaf Karagila: Preservation theorems for symmetric extensions and Krivine-style results
Kurt Godel Research Center
5/21/2019
Jean-Louis Krivine has used methods of realizability to prove several new independence results in ZF+DC. We show how to obtain some of these results using classical methods.
For the proof we also need theorems which lets us preserve some bits of choice in symmetric extensions. One of these theorems is an old folklore result, and the other is a new theorem.
This will be our final newsletter for the Spring 2019 semester - regular mailings will resume at the end of August. Special announcements may be sent in the interim as events warrant.
Have a great summer,
Jonas
This Week in Logic at CUNY:
- - - - Tuesday, May 21, 2019 - - - -
ASL 2019 Annual Meeting
May 20 — 23
CUNY Graduate Center
The Association for Symbolic Logic will have its 2019 North American Annual Meeting at the CUNY Graduate Center from May 20th through the 23rd. Additional information, including a schedule of speakers, is available on their website.
Aim: Weak Arithmetics play a fundamental role in several areas of philosophy, mathematics, and computer science by studying the nature and properties of natural numbers from a logical point of view. The aim of the conference is to provide a forum for researchers to present their results to members of communities who study or apply weak arithmetics in various fields and formalisms.
Topics: Proofs in arithmetic with restricted system of axioms. Non-standard models of such systems. Decidability, undecidability, and complexity of arithmetical theories. Definability in arithmetic structures. Machines, automata and words related to arithmetic. Finite model theory, word structures.
Invited Speakers: Gabriel Conant (Notre Dame), Damir Dzhafarov (University of Connecticut), Victoria Gitman (CUNY), Matt Kaufmann (University of Texas), Chris Miller (The Ohio State University), Russell Miller (CUNY), Arseniy Sheydvasser (CUNY).
Many thanks to Victoria Gitman for her development work!
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Piotr Koszmider; Lifting uncountable combinatorics to the Banach space level: Banach spaces C(K) with few operators. Part 1.
IMPAN Working Group in Applications of Set Theory
5/19/2019
Seminar: Working group in applications of set theory, IMPAN
Thursday, 23.05.2019, 10:15, room 105, IMPAN
Speaker: Piotr Koszmider (IMPAN)
Title: "Lifting uncountable combinatorics to the Banach space level: Banach spaces C(K) with few operators. Part 1."
Abstact: "This series of 4 talks will be a minicourse on Banach spaces of continuous functions which have few operators, projections, injections etc. In particular they can be indecomposable and nonisomorphic with their hyperplanes. To obtain this linear operator level rigidity one needs to construct compact Ks which are not only rigid in the usual sense, i.e., in terms of continuous mappings on K. One needs to deal with weak* continuous functions from K into the space M(K) of Radon measures on K, so the combinatorics of the constructions needs stronger conditions than for endo-rigid Boolean algebras or strongly rigid compact spaces. We will present main arguments leading to C(K)s with the required properties but the proofs of many lemmas will be omitted. The talks should be accessible to everyone with general analytic and topological background.".
Visit our seminar page which may include some future talks at https://www.impan.pl/~set_theory/Seminar/
Wednesday seminar
Prague Set Theory Seminar
5/15/2019
Dear all,
The seminar meets on Wednesday May 22nd at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Jonathan Verner -- The RK ordering on P-points
Best,
David
This Week in Logic at CUNY
This Week in Logic at CUNY
5/12/2019
This Week in Logic at CUNY:
- - - - Monday, May 13, 2019 - - - -
Logic and Metaphysics Workshop
Date: Monday, May 13th, 4.15-6.15
Place: Room 7314, CUNY Graduate Center
Speaker: Martina Botti (Columbia)
Title: Composition as Identity: A New Approach
Abstract: I argue that the debate on composition as identity – the thesis that any composite object is identical to its parts – is deadlocked because both the defenders and the detractors of the claim have so far defended and criticized respectively something that is not composition as identity. After having made clear how composition as identity should properly be understood, I will set forth a new strategy to defend it.
- - - - Tuesday, May 14, 2019 - - - -
- - - - Wednesday, May 15, 2019 - - - -
The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York
Speaker: Sergei Artemov, The Graduate Center, CUNY.
Date and Time: Wednesday May 15, 2019, 7:00 - 8:30 PM., Room 6417.
Title: On the Provability of Consistency.
Abstract: We revisit the foundational question concerning Peano arithmetic PA:
(1) can consistency of PA be established by means expressible in PA?
The usual answer to (1) is “No, by Gödel’s Second Incompleteness Theorem.” In that theorem (G2), Gödel used an arithmetization of contentual mathematical reasoning and established that the arithmetical formula representing PA-consistency is not derivable in PA. Applying G2 to (1), one makes use of the formalization thesis (FT):
FT: any proof by means expressible in PA admits Gödel’s arithmetization.
Historically, there has been no consensus on FT; Gödel (1931) and Hilbert (1934) argued against an even weaker version of FT with respect to finitary proofs, whereas von Neumann accepted it.
Note that the aforementioned negative answer to (1) is unwarranted: here is a counter-example to FT. Let Ind(F) denote the induction statement for an arithmetical formula F. The claim C, “for each formula F, Ind(F),” is directly provable by means of PA: given any F, argue by induction to establish Ind(F). However, C is not supported by any arithmetization as a single formula since PA is not finitely axiomatizable.
We provide a positive answer to (1). We offer a mathematical proof of PA-consistency,
No finite sequence of formulas is a PA-proof of 0=1,
by means expressible in PA, namely, by partial truth definitions. Naturally, this proof does not admit Gödel’s arithmetization either.
- - - - Thursday, May 16, 2019 - - - -
*** CUNY Final Exams begin today ***
- - - - Friday, May 17, 2019 - - - -
Set Theory Seminar (RESCHEDULED from April 12)
CUNY Graduate Center, Room 6417
Friday, May 17, 10:00-11:45am
Jonas Reitz, CUNY
Generalized Cohen Iterations
Adding Cohen subsets to each of a class of cardinals in turn is a common construction in set theory, and underlies many fundamental results. The construction comes in two basic flavors, products (as in Easton’s Theorem on the powers of regular cardinals) and iterations (forcing the GCH). These flavors are apparently quite similar, forcing at stage kappa to add subsets via the Cohen partial order Add(kappa,lambda). They differ only in the universe over which Add(kappa,lambda) is defined - in the case of products the ground model poset is used at each stage, whereas in typical iterations the poset is taken from the partial extension up to kappa. In this talk I will consider an alternative, in which we allow Add(kappa,lambda) to be defined over an arbitrary inner model (lying between the ground model and the extension up to kappa) at each stage. These generalized Cohen iterations are ZFC-preserving, although neither the proof for products nor for traditional iterations transfers directly. They allow constructions such as class iterations of class products of Cohen forcing, with applications including new work with Kameryn Williams on iterating the Mantle.
Next Week in Logic at CUNY:
- - - - Monday, May 20, 2019 - - - -
Logic and Metaphysics Workshop
Date: Monday, May 20th, 4.15-6.15
Place: Room 7314, CUNY Graduate Center
Speaker: Vincent Peluce (CUNY)
Title: The Perception of Time in Intuitionistic Arithmetic
Abstract: In L.E.J. Brouwer’s first act of intuitionism, the subject’s perception of time is put forth as the foundation on which arithmetic will be built. According to Brouwer, proper intuitionistic arithmetic, as with the rest of intuitionistic mathematics, is not tied to any particular formal system. When we try to axiomatically approximate an intuitionistic arithmetical system, we are faced with the problem of incorporating the subject and their perception into the axiom system itself. We discuss some unsatisfactory responses to this problem and then offer a solution.
ASL 2019 Annual Meeting
May 20 — 23
CUNY Graduate Center
The Association for Symbolic Logic will have its 2019 North American Annual Meeting at the CUNY Graduate Center from May 20th through the 23rd. Additional information, including a schedule of speakers, is available on their website.
The Association for Symbolic Logic will have its 2019 North American Annual Meeting at the CUNY Graduate Center from May 20th through the 23rd. If you would like to attend, you are asked to register by May 6th. Additional information, including a schedule of speakers, is available on their website.
Aim: Weak Arithmetics play a fundamental role in several areas of philosophy, mathematics, and computer science by studying the nature and properties of natural numbers from a logical point of view. The aim of the conference is to provide a forum for researchers to present their results to members of communities who study or apply weak arithmetics in various fields and formalisms.
Topics: Proofs in arithmetic with restricted system of axioms. Non-standard models of such systems. Decidability, undecidability, and complexity of arithmetical theories. Definability in arithmetic structures. Machines, automata and words related to arithmetic. Finite model theory, word structures.
Invited Speakers: Gabriel Conant (Notre Dame), Damir Dzhafarov (University of Connecticut), Victoria Gitman (CUNY), Matt Kaufmann (University of Texas), Chris Miller (The Ohio State University), Russell Miller (CUNY), Arseniy Sheydvasser (CUNY).
Many thanks to Victoria Gitman for her development work!
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BLAST 2019, Boulder, May 20-24
Conference
5/9/2019
conference: BLAST 2019
date: May 20-24, 2019
location: University of Colorado, Boulder CO
web: https://math.colorado.edu/blast/2019/
email: blast2019@colorado.edu
SCOPE
The BLAST conference series focuses on related areas within the
foundations of mathematics, specifically Boolean Algebras,
Lattice Theory, Algebraic Logic, Universal Algebra, Set Theory,
and Set-theoretic and Point-free Topology.
This year's installment of BLAST will take place at the University
of Colorado at Boulder. The scientific program will include invited
lectures, tutorial lectures and 20-minute contributed talks. The
central BLAST web page, with links to past meetings, can be found here:
http://math.colorado.edu/blast/
BLAST 2019 INVITED SPEAKERS:
Guram Bezhanishvili (New Mexico State University)
Will Brian (University of North Carolina at Charlotte)
Ronnie Chen (University of Illinois at Urbana-Champaign)
Miklos Maroti (University of Szeged)
Ralph McKenzie (Vanderbilt University)
Matt Moore (University of Kansas)
Tommaso Moraschini (Czech Academy of Sciences)
Adam Prenosil (Vanderbilt University)
Douglas Ulrich (University of California at Irvine)
Amanda Vidal (Czech Academy of Sciences)
Ross Willard (University of Waterloo)
REGISTRATION INFORMATION
Registration is open at
https://math.colorado.edu/blast/2019/registration.html
Early registration helps in our planning.
The fee will be $80, and is payable only at the conference, in cash.
SUPPORT REQUESTS
There will be limited funds to support the participation of graduate
students and recent PhD's. Instructions for submitting a funding
request can be found on the conference web site.
ABSTRACT SUBMISSION
In addition to the invited talks and tutorial presentations, there will
be 20-minute contributed presentations. Information on the submission
procedures for titles and abstracts can be found at the conference web site.
ACCOMMODATIONS
Please visit the conference website at
https://math.colorado.edu/blast/2019/
DATES
May 13, 2019: Abstract submission deadline
May 20-24, 2019: Conference
THANKS
BLAST 2019 is supported by NSF, the Research and Innovation Office
of the University of Colorado, and the Department of Mathematics
of the University of Colorado.
LOCAL ORGANIZERS
William DeMeo, Keith Kearnes, Peter Mayr, Agnes Szendrei
Tagged: Guram Bezhanishvili, Will Brian, Ronnie Chen,
Miklos Maroti, Ralph McKenzie, Matt Moore, Tommaso Moraschini, Adam Prenosil, Douglas Ulrich, Amanda Vidal, Ross Willard
Mexwell Levine: Partitions of Reflecting Stationary Sets
Prague Set Theory Seminar
5/8/2019
Dear all,
The seminar meets on Wednesday May 15th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Mexwell Levine -- Partitions of Reflecting Stationary Sets
Abstract attached.
Best,
David
Tagged: Maxwell Levine
Arturo Martínez-Celis; Choice vs Determinacy
IMPAN Working Group in Applications of Set Theory
5/6/2019
Seminar: Working group in applications of set theory, IMPAN
NOTE THE USUAL TIME AND PLACE:
Thursday, 09.05.2019, 10:15, room 105, IMPAN
Speaker: Arturo Martínez-Celis (IMPAN)
Title: "Choice vs Determinacy"
Abstact: "We will discuss the concept of infinite game and winning strategies and we will present some examples, theorems and applications to topology. In particular we will prove that every uncountable Borel set has a homeomorphic copy of the Cantor set. The axiom of determinacy (AD) states that for certain kind of games, the Gale-Stewart games, one player has always a winning strategy. The aim of this talk is to present the differences between the universes satisfying AD and the universes satisfying the axiom of choice".
Visit our seminar page which may include some future talks at https://www.impan.pl/~set_theory/Seminar/
Tagged: Arturo Martínez-Celis
Logic Seminar 8 May 2019 17:00 hrs at NUS
NUS Logic Seminar
5/6/2019
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 8 May 2019, 17:00 hrs
Room: S17#04-05, Department of Mathematics, NUS
Speaker: Borisa Kuzeljevic
Title: Matrices of countable elementary submodels
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
We present an application of the forcing notion of finite
matrices whose rows consist of isomorphic countable elementary
submodels of a given structure of the form H_theta.
We will explain how forcing with this poset adds a Kurepa tree. If a
minor modification of the poset is considered, then the tree added is
actually an almost Souslin Kurepa tree.
This is a joint work with Stevo Todorcevic.
Tagged: Borisa Kuzeljevic
This Week in Logic at CUNY
This Week in Logic at CUNY
5/5/2019
This Week in Logic at CUNY:
- - - - Monday, May 6, 2019 - - - -
Logic and Metaphysics Workshop
Date: Monday, May 6th, 4.15-6.15
Place: Room 7314, CUNY Graduate Center
Speaker: Daniel Durante (Natal)
Title: No Metaphysical Disagreement Without Logical Incompatibility
Abstract: The purpose of this talk is to defend the logical incompatibility of the opposing views as a criterion for characterizing disagreements as genuinely metaphysical. That is, I intend to argue that a specific dispute is a metaphysical disagreement only when the conflicting views are governed by different logics. If correct, this criterion would not only help to separate merely verbal from genuine metaphysical debates, but it also would ground an argument against deflationism, guaranteeing the substantiality and relevance of metaphysics. I intend to clarify the criterion, to present its basic foundations and commitments, to give some logical and metaphysical motivations for its adoption and some examples of its application.
- - - - Tuesday, May 7, 2019 - - - -
- - - - Wednesday, May 8, 2019 - - - -
The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York
Speaker: Jonathan Funk, Queensborough Community College.
Date and Time: Wednesday May 8, 2019, 7:00 - 8:30 PM., Room 6417.
Title: Isotropy theory meets Galois theory.
Abstract: Isotropy theory for toposes is about internal symmetry of a topos. A topos may have trivial isotropy, said to be anisotropic. For example, a localic topos is anisotropic. The isotropy of a topos may be cancelled to yield what we call the isotropy quotient of a topos, although the quotient may itself have isotropy, or what we call higher isotropy of the given topos. (By analogy, the quotient of a group by its center may itself have non-trivial center.) Let us say that a topos is locally anisotropic if it has an etale cover by an anisotropic topos.
THEOREM: A locally anisotropic topos has no higher isotropy. Equivalently, its isotropy quotient is anisotropic. Furthermore, a locally anisotropic topos is recovered as the topos of actions for a connected groupoid internal to its isotropy quotient.
COROLLARY: An etendue, or locally localic topos, has no higher isotropy. An etendue may be recovered as the topos of actions for a connected groupoid internal to its isotropy quotient.
Our argumentation of the theorem brings into focus how isotropy theory and Galois theory for toposes meet in a natural and evidently effective way.
Joint work with Pieter Hofstra.
- - - - Thursday, May 9, 2019 - - - -
Computer Science Colloquium
THURSDAY, May 9TH, 2019, 4:15pm – 6:15pm
Room 9205
Larry Moss, Indiana University
Bridging the Gap Between Logic and Machine Learning in Natural Language Inference
Abstract: The field of natural language inference (NLI) has seen strong progress in recent years, especially after the advent of deep learning. The basic goal is to see whether one natural language (NL) sentence “follows from” another, and to do this on a computer, for sentences “in nature”. Reflecting my own background, I wondered if there was anything whatsoever which 2000+years of work in logic could contribute to NLI.
This talk details work on making a connection between logic and computational linguistics. It will touch on topics such as: combinatory categorical grammar and its syntax-semantics interference; work on monotonicity pioneered by Johan van Benthem; the typed lambda calculus; natural logic, and algorithms from it; datasets like SICK, FraCaS, and SNLI; and the bidirectional language model BERT.
The goal is to see whether theory scales up to practice. I won’t give away the end of the story here, but suffice it to say the we are finding this work to be both challenging and interesting.
- - - - Friday, May 10, 2019 - - - -
Set Theory Seminar
CUNY Graduate Center, Room 6417
Friday, May 10, 10:00-11:45am
Kameryn Williams, University of Hawai‘i at Mānoa Transfinite Recursion from Gödel–Bernays to Kelley–Morse
Gödel–Bernays set theory GB and Kelley–Morse set theory KM are two formal theories for second-order set theory, allowing both sets and proper classes as objects. GB is the weaker of the two theories, being conservative over ZF, while KM is the stronger. Set theorists have used KM in applications where GB is not strong enough; for instance, Kunen formulated his celebrated inconsistency result in the context of KM, as KM has the resources to directly allow talk of elementary embeddings of the universe of sets. But weaker theories than KM suffice for many of these applications. Between GB and KM there is a hierarchy of intermediate theories based upon restricting the logical complexity allowed in the comprehension axiom.
In this talk I will present a hierarchy of second-order set theories which refines the comprehension-based hierarchy. This hierarchy is based upon transfinite recursion principles, ordered first by the logical complexity of the properties allowed and second by the lengths of well-orders on which we may carry out the recursions. Theories in this hierarchy are separated in terms of consistency strength. The substantive new result to establish this hierarchy is the following: Let kk be a natural number. Suppose (M,X)(M,X) satisfies GB and that Γ∈XΓ∈X is a class well-order which is closed under addition. In case k=0k=0 further assume Γ≥ωωΓ≥ωω. Then, if (M,X)(M,X) satisfies Π1kΠk1-Transfinite Recursion for recursions along ΓΓ, there is Y⊆XY⊆X coded in XX so that (M,Y)(M,Y) satisfies GB plus the principle of Π1kΠk1-Transfinite Recursion for recursions along well-orders of length <Γ<Γ.
Model Theory Seminar
CUNY Graduate Center, Room 6417
Friday, May 10, 12:30-2:00pm
Alexander Van Abel, CUNY
Asymptotic Classes of Finite Structures
A one-dimensional asymptotic class, as introduced by Macpherson and Steinhorn in 2008, is a collection of finite structures whose definable subsets in a single variable grow approximately linearly with respect to the size of the structure, in a definable and well-behaved fashion. The motivating example is the collection of finite fields, as proved by Chatzidakis, van den Dries and Macintyre in 1992. In this talk, we survey Steinhorn and Macpherson's foundational 2008 paper. We give examples and nonexamples of one-dimensional asymptotic classes, as well as more general notions such as N-dimensional and multidimensional classes. We show how infinite ultra-products of one-dimensional asymptotic classes are model-theoretically nice, with particular emphasis on the existence of a well-behaved dimension and measure on definable subsets and the consequences of such.
Next Week in Logic at CUNY:
- - - - Monday, May 13, 2019 - - - -
Logic and Metaphysics Workshop
Date: Monday, May 13th, 4.15-6.15
Place: Room 7314, CUNY Graduate Center
Speaker: Martina Botti (Columbia)
Title: Composition as Identity: A New Approach
Abstract: I argue that the debate on composition as identity – the thesis that any composite object is identical to its parts – is deadlocked because both the defenders and the detractors of the claim have so far defended and criticized respectively something that is not composition as identity. After having made clear how composition as identity should properly be understood, I will set forth a new strategy to defend it.
- - - - Tuesday, May 14, 2019 - - - -
- - - - Wednesday, May 15, 2019 - - - -
The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York
Speaker: Sergei Artemov, The Graduate Center, CUNY.
Date and Time: Wednesday May 15, 2019, 7:00 - 8:30 PM., Room 6417.
Title: On the Provability of Consistency.
Abstract: We revisit the foundational question concerning Peano arithmetic PA:
(1) can consistency of PA be established by means expressible in PA?
The usual answer to (1) is “No, by Gödel’s Second Incompleteness Theorem.” In that theorem (G2), Gödel used an arithmetization of contentual mathematical reasoning and established that the arithmetical formula representing PA-consistency is not derivable in PA. Applying G2 to (1), one makes use of the formalization thesis (FT):
FT: any proof by means expressible in PA admits Gödel’s arithmetization.
Historically, there has been no consensus on FT; Gödel (1931) and Hilbert (1934) argued against an even weaker version of FT with respect to finitary proofs, whereas von Neumann accepted it.
Note that the aforementioned negative answer to (1) is unwarranted: here is a counter-example to FT. Let Ind(F) denote the induction statement for an arithmetical formula F. The claim C, “for each formula F, Ind(F),” is directly provable by means of PA: given any F, argue by induction to establish Ind(F). However, C is not supported by any arithmetization as a single formula since PA is not finitely axiomatizable.
We provide a positive answer to (1). We offer a mathematical proof of PA-consistency,
No finite sequence of formulas is a PA-proof of 0=1,
by means expressible in PA, namely, by partial truth definitions. Naturally, this proof does not admit Gödel’s arithmetization either.
- - - - Thursday, May 16, 2019 - - - -
*** CUNY Final Exams begin today ***
- - - - Friday, May 17, 2019 - - - -
Set Theory Seminar (RESCHEDULED from April 12)
CUNY Graduate Center, Room 6417
Friday, May 17, 10:00-11:45am
Jonas Reitz, CUNY
Generalized Cohen Iterations
Adding Cohen subsets to each of a class of cardinals in turn is a common construction in set theory, and underlies many fundamental results. The construction comes in two basic flavors, products (as in Easton’s Theorem on the powers of regular cardinals) and iterations (forcing the GCH). These flavors are apparently quite similar, forcing at stage kappa to add subsets via the Cohen partial order Add(kappa,lambda). They differ only in the universe over which Add(kappa,lambda) is defined - in the case of products the ground model poset is used at each stage, whereas in typical iterations the poset is taken from the partial extension up to kappa. In this talk I will consider an alternative, in which we allow Add(kappa,lambda) to be defined over an arbitrary inner model (lying between the ground model and the extension up to kappa) at each stage. These generalized Cohen iterations are ZFC-preserving, although neither the proof for products nor for traditional iterations transfers directly. They allow constructions such as class iterations of class products of Cohen forcing, with applications including new work with Kameryn Williams on iterating the Mantle.
- - - - Other Logic News - - - -
Please take note of two upcoming conferences this month at CUNY's Graduate Center:
The Association for Symbolic Logic will have its 2019 North American Annual Meeting at the CUNY Graduate Center from May 20th through the 23rd. If you would like to attend, you are asked to register by May 6th. Additional information, including a schedule of speakers, is available on their website.
Aim: Weak Arithmetics play a fundamental role in several areas of philosophy, mathematics, and computer science by studying the nature and properties of natural numbers from a logical point of view. The aim of the conference is to provide a forum for researchers to present their results to members of communities who study or apply weak arithmetics in various fields and formalisms.
Topics: Proofs in arithmetic with restricted system of axioms. Non-standard models of such systems. Decidability, undecidability, and complexity of arithmetical theories. Definability in arithmetic structures. Machines, automata and words related to arithmetic. Finite model theory, word structures.
Invited Speakers: Gabriel Conant (Notre Dame), Damir Dzhafarov (University of Connecticut), Victoria Gitman (CUNY), Matt Kaufmann (University of Texas), Chris Miller (The Ohio State University), Russell Miller (CUNY), Arseniy Sheydvasser (CUNY).
Many thanks to Victoria Gitman for her development work!
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No set theory seminar this week
Toronto Set Theory Seminar
5/3/2019
Hi everyone!
We will not have a seminar this week.
See you soon!
Osvaldo Guzman
F_sigma Games of Length omega^2
Bristol Logic Seminar
4/30/2019
1st May 2019, 4:00 pm – 5:00 pm
Howard House, 2nd Floor Seminar Room
Speaker: Juan Aguilera (Technische Universität Vienna)
Title: Open graphs and hypergraphs on definable subsets of generalized Baire spaces
Abstract:
We show, in ZFC, that the determinacy of F_sigma games of length omega^2 is equivalent to the existence of an admissible model of AD that contains R and reflects Pi_1 statements about the next admissible set.
Set Theory in the United Kingdom is a joint research group in set theory funded by the London Mathematical Society (Scheme 3) with members at the Universities of Bristol, Cambridge, East Anglia, Leeds, Oxford, Warwick and University College London.
STUK 2 will take place on Wednesday, 8 May 2019, 11.00-18.00 at the University of Bristol.
11-12 Victoria Gitman: Set theory in second-order
13-14 Andrew Brooke-Taylor: Set theory and category theory
Location: 4th floor seminar room, School of Mathematics, University of Bristol, Howard house, Queen’s avenue, Bristol BS8 1SD.
8th May 2019, 11:00 am – 12:00 pm
Howard House, 4th Floor Seminar Room
Speaker: Victoria Gitman (CUNY)
Title: Set theory in second-order
Abstract:
Classes, from class forcing notions to elementary embeddings of the universe to inner models, play a fundamental role in modern set theory. But within first-order set theory we are limited to studying only definable classes and we cannot even express properties that necessitate quantifying over classes. Second-order set theory is a formal framework in which a model consists both of a collection of sets and a collection of classes (which are themselves collections of sets). In second-order set theory, we can study classes such as truth predicates, which can never be definable over a model of ZFC, and properties that, for instance, quantify over all inner models. With this formal background we can develop a theory of class forcing that explains why and when class forcing behaves differently from set forcing. In this talk, I will discuss a hierarchy of second-order set theories, starting from the weak Gödel-Bernays set theory GBC and going beyond the relatively strong Kelley-Morse theory KM. I will give an overview of a number of interesting second-order set theoretic principles that arose out of recent work in this area, such as, class choice principles, transfinite recursion with classes, determinacy of games on the ordinals, and the class Fodor Principle. The study of where these principles fit in the hierarchy of second-order set theories should serve as the beginning of a reverse mathematics program that I hope this talk will encourage set theorists to take part in.
8th May 2019, 11:00 am – 12:00 pm
Howard House, 4th Floor Seminar Room
Speaker: Andrew Brooke-Taylor (University of Leeds)
Title: Set theory and category theory
Abstract:
Classes, from class forcing notions to elementary embeddings of the universe to inner models, play a fundamental role in modern set theory. But within first-order set theory we are limited to studying only definable classes and we cannot even express properties that necessitate quantifying over classes. Second-order set theory is a formal framework in which a model consists both of a collection of sets and a collection of classes (which are themselves collections of sets). In second-order set theory, we can study classes such as truth predicates, which can never be definable over a model of ZFC, and properties that, for instance, quantify over all inner models. With this formal background we can develop a theory of class forcing that explains why and when class forcing behaves differently from set forcing. In this talk, I will discuss a hierarchy of second-order set theories, starting from the weak Gödel-Bernays set theory GBC and going beyond the relatively strong Kelley-Morse theory KM. I will give an overview of a number of interesting second-order set theoretic principles that arose out of recent work in this area, such as, class choice principles, transfinite recursion with classes, determinacy of games on the ordinals, and the class Fodor Principle. The study of where these principles fit in the hierarchy of second-order set theories should serve as the beginning of a reverse mathematics program that I hope this talk will encourage set theorists to take part in.
13th May 2019, 2:30 pm – 3:30 pm
Howard House, 4th Floor Seminar Room
Speaker: Adam Epstein (University of Warwick )
Title: Axioms of Infinity in Zermelo Set Theory
Abstract:
We show that without Replacement one cannot infer the existence of a definite infinite set from the existence of an otherwise unspecified infinite set.
Philipp Lücke: Simple definitions of complicated sets
Kurt Godel Research Center
4/29/2019
For many types of pathological sets of real numbers (i.e. sets of reals constructed with the help of the Axiom of Choice), it is possible to use results from descriptive set theory to show that these sets cannot be defined by simple formulas in second-order arithmetic.
In this talk, I want to present results dealing with the set theoretic definability of pathological objects, i.e. with the question whether objects usually obtained from the Axiom of Choice can be defined in the structure $\langle\mathrm{V},\in\rangle$ using simple formulas.
I will focus on the definability of well-orderings of the reals and bistationary subsets of uncountable regular cardinals.
Title: A Mechanistic Conception of Metaphysical Grounding
Abstract: A dominant theoretical framework in philosophy of science employs the notion of mechanistic dependence to elucidate how higher-level, less fundamental phenomena depend upon and arise out of lower-level, more fundamental phenomena. To elucidate the same thing, literature in metaphysics employs the notion of grounding. As I argue, regardless of whether the notion of mechanistic dependence or the notion of grounding is used to theoretically portray how higher-level phenomena arise out of lower-level phenomena, what is captured by such portrayals is the same. Thus, these notions pick out the same features of the world. With this as my basis, I identify the notion of grounding with the notion of mechanistic dependence, and thus, construct a mechanistic conception of grounding. Since mechanistic dependence is understood in terms of mechanisms, my conception frames grounding in terms of mechanisms. Moreover, the contemporary notion of mechanisms is shaped by how mechanisms are represented via the mechanistic models and mechanistic explanations provided by science. Thus, because my conception grounding identifies grounding with mechanistic dependence and thereby frames grounding in terms of mechanisms, this conception suggests that the notion of grounding is to be tailored to and constrained by the mechanistic models and mechanistic explanations provided by science. This leads the mechanistic conception of grounding to reject a wide variety of conventional claims about grounding, and thus, to offer a treatment of grounding that is highly revisionary. To reinforce the plausibility of the mechanistic conception of grounding, I discuss how grounding and mechanistic dependence are associated with explanation. Whereas mechanistic dependence is associated with mechanistic explanation, grounding is associated with grounding explanation. For each kind of explanation, some higher-level phenomenon P is explained by appeal to some low-level phenomenon that Parises out of. As I argue, these forms of explanation can be plausibly identified. This greatly supports the mechanistic conception of grounding. For if grounding explanations employ the notion of grounding and mechanistic explanations employ the notion of mechanistic explanation, and these forms of explanation can be identified, this suggests that these explanations employ the same notion. And, just as the notions of grounding and mechanistic dependence capture the same connection between higher-level and lower-level phenomena, grounding explanation and mechanistic explanation do so as well. Finally, to argue that the mechanistic conception is to be preferred to standard conceptions, I argue that my conception offers a powerful defense of grounding from recent criticisms.
- - - - Tuesday, Apr 30, 2019 - - - -
- - - - Wednesday, May 1, 2019 - - - -
- - - - Thursday, May 2, 2019 - - - -
- - - - Friday, May 3, 2019 - - - -
Set Theory Seminar
CUNY Graduate Center, Room 6417
Friday, May 3, 10:00-11:45am
Joseph Van Name, CUNY Lower bounds on the cardinalities of quotient algebras of elementary embeddings
From non-trivial elementary embeddings j1…jr:Vλ→Vλj1…jr:Vλ→Vλ, we obtain a sequence of polynomials (pn(x1,…,xr))n∈ω(pn(x1,…,xr))n∈ω that satisfies the infinite product∞∏k=0pk(x1,…,xr)=11−(x1+⋯+xr).∏k=0∞pk(x1,…,xr)=11−(x1+⋯+xr).From this infinite product, we deduce lower bounds of the cardinality of |⟨j1,...,jr⟩/≡α||⟨j1,...,jr⟩/≡α| using analysis and analytic number theoretic techniques. Computer calculations that search for Laver-like algebras give some empirical evidence that these lower bounds cannot be greatly improved.
Model Theory Seminar
CUNY Graduate Center, Room 6417
Friday, May 3, 12:30-2:00pm
Artem Chernikov, UCLA
TBA
Logic Workshop
CUNY Graduate Center, Room 6417
Friday, May 3, 2:00-3:30pm
Gregory Cherlin, Rutgers University Countable universal graphs with forbidden subgraphs
Abstract
Definition: A collection FF of forbidden subgraphs is a Rado family if the class of countable FF-free graphs contains a universal structure with respect to embeddings as induced subgraphs. (By 'forbidden' I mean forbidden as subgraphs; usage varies in the literature.)
We consider the following decision problem for Rado families.
Problem: Given a finite set FF of finite, connected graphs, determine whether or not it is a Rado family.
Question: Is this a decidable problem?
If we specialize to the sake of a single constraint then we speak instead of a Rado constraint. Much is known, and much more conjectured, about the case of a single constraint.
Conjecture: The decision problem for the case of a single constraint is decidable.
Discussion
From the model theoretic side, a finite collection of forbidden subgraphs specifies a universal theory with some special properties: notably, there is a model companion. When we restrict to families of connected constraints, the theory has joint embedding and the model companion is complete. In model theoretic terms the question becomes whether the model companion has a countable universal model with respect to elementary embedding, for which a purely type theoretic criterion is known.
Decision problems for other model theoretic properties of the model companion are natural. We have focused on this one because the question came to us from graph theory. However, even in that form, two variants are relevant.
Can we decide whether the model companion is ℵ0ℵ0-categorical?
Dropping the connectedness hypothesis on the constraints, can we decide whether the model companion is complete?
The main source of positive answers to the universality problem appears to be the ℵ0ℵ0-categorical case, and this has some theoretical justification. The most direct route to understanding the original graph theoretical problem appears to take the detour through ℵ0ℵ0-categoricity.
As time allows, I would like to discuss the following three points.
What we know, and what we expect, in the case of a single constraint;
Methods of proof (algebraic closure; induction by pruning);
The status of the decision problem for j.e.p. and its analog in the theory of permutation pattern classes (work of Braunfeld).
This is joint work with Shelah, e.g. [Sh689].
Next Week in Logic at CUNY:
- - - - Monday, May 6, 2019 - - - -
- - - - Tuesday, May 7, 2019 - - - -
- - - - Wednesday, May 8, 2019 - - - -
The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York
Speaker: Jonathan Funk, Queensborough Community College.
Date and Time: Wednesday May 8, 2019, 7:00 - 8:30 PM., Room 6417.
Title: Isotropy theory meets Galois theory.
Abstract: Isotropy theory for toposes is about internal symmetry of a topos. A topos may have trivial isotropy, said to be anisotropic. For example, a localic topos is anisotropic. The isotropy of a topos may be cancelled to yield what we call the isotropy quotient of a topos, although the quotient may itself have isotropy, or what we call higher isotropy of the given topos. (By analogy, the quotient of a group by its center may itself have non-trivial center.) Let us say that a topos is locally anisotropic if it has an etale cover by an anisotropic topos.
THEOREM: A locally anisotropic topos has no higher isotropy. Equivalently, its isotropy quotient is anisotropic. Furthermore, a locally anisotropic topos is recovered as the topos of actions for a connected groupoid internal to its isotropy quotient.
COROLLARY: An etendue, or locally localic topos, has no higher isotropy. An etendue may be recovered as the topos of actions for a connected groupoid internal to its isotropy quotient.
Our argumentation of the theorem brings into focus how isotropy theory and Galois theory for toposes meet in a natural and evidently effective way.
Joint work with Pieter Hofstra.
- - - - Thursday, May 9, 2019 - - - -
- - - - Friday, May 10, 2019 - - - -
Set Theory Seminar
CUNY Graduate Center, Room 6417
Friday, May 10, 10:00-11:45am
Kameryn Williams, University of Hawai‘i at Mānoa Transfinite Recursion from Gödel–Bernays to Kelley–Morse
Gödel–Bernays set theory GB and Kelley–Morse set theory KM are two formal theories for second-order set theory, allowing both sets and proper classes as objects. GB is the weaker of the two theories, being conservative over ZF, while KM is the stronger. Set theorists have used KM in applications where GB is not strong enough; for instance, Kunen formulated his celebrated inconsistency result in the context of KM, as KM has the resources to directly allow talk of elementary embeddings of the universe of sets. But weaker theories than KM suffice for many of these applications. Between GB and KM there is a hierarchy of intermediate theories based upon restricting the logical complexity allowed in the comprehension axiom.
In this talk I will present a hierarchy of second-order set theories which refines the comprehension-based hierarchy. This hierarchy is based upon transfinite recursion principles, ordered first by the logical complexity of the properties allowed and second by the lengths of well-orders on which we may carry out the recursions. Theories in this hierarchy are separated in terms of consistency strength. The substantive new result to establish this hierarchy is the following: Let kk be a natural number. Suppose (M,X)(M,X) satisfies GB and that Γ∈XΓ∈X is a class well-order which is closed under addition. In case k=0k=0 further assume Γ≥ωωΓ≥ωω. Then, if (M,X)(M,X) satisfies Π1kΠk1-Transfinite Recursion for recursions along ΓΓ, there is Y⊆XY⊆X coded in XX so that (M,Y)(M,Y) satisfies GB plus the principle of Π1kΠk1-Transfinite Recursion for recursions along well-orders of length <Γ<Γ.
- - - - Other Logic News - - - -
Conference announcement:
Model Theory and Mathematical Logic, in honor of Chris Laskowski's 60th birthday, June 21 - 23, 2019, at The University of Maryland, College Park http://www.umdlogic2019.com/
The 2019 Boise Extravaganza in Set Theory will take place in Ashland, Oregon, on the campus of Southern Oregon University, during June 19-21.
We are currently welcoming applications for travel grants from graduate students and postdocs (and other categories) in set theory and related fields. We will begin considering applications on May 1. We will continue accepting applications on a rolling basis until May 31.
Plenary speakers:
Dana Bartosova (University of Florida) Steve Jackson (University of North Texas) Reese Johnston (University of Washington Robinson Center) Assaf Shani (UCLA) Piotr Szeczwak (Cardinal Stefan Wyszyński University, Warsaw)
The BEST conference particularly aims to support the careers of young researchers in set theory (and related fields!), with travel support available for graduate students and postdocs. BEST features professional development opportunities and awards for student presentations. Please pass this invitation along to students, postdocs, and colleagues to submit an abstract and participate in BEST!
BEST is an international conference featuring talks on a broad range of recent advances in set theory research. The conference is organized by the Set Theory group at Boise State University and is structured as a symposium of the 100th annual meeting of the American Association for the Advancement of Science, Pacific Division (AAAS-PD). BEST is also supported by the NSF and Boise State University.
Organizers: Liljana Babinkostova (Boise State University), John Clemens (Boise State University), Samuel Coskey (Boise State University), Marion Scheepers (Boise State University). Scientific Committee: Natasha Dobrinen (University of Denver), Simon Thomas (Rutgers University)
Many thanks to Victoria Gitman for her development work!
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SPECIAL UPDATE: This Week in Logic at CUNY
This Week in Logic at CUNY
4/24/2019
Hi everyone,
Please note the addition of this Friday's talk in the Columbia Seminar on Logic Probability and Games.
All the best,
Jonas
This Week in Logic at CUNY:
- - - - Thursday, Apr 25, 2019 - - - -
- - - - Friday, Apr 26, 2019 - - - -
Message from Prof Haim Gaifman, Columbia University The Columbia Seminar Logic Probability and Games
will meet this coming Friday April 26, 4:10-6:00, at the Faculty House (for direction to the Faculty house click the link at the bottom).
Professor Simon Huttegger will give a talk entitled “Rethinking Convergence to the Truth”. In this talk he uses the framework of Robinson’s non-standard analysis, which makes it possible to use infinitesimals as they have been used by Leibniz (and other non-standard notions of the calculus and probability theory), in order to throw light on problems arising in Bayesian probability theory, and in the philosophy of science.
Professor Huttegger, who teaches Logic and Philosophy of Science at UC Irvine, is a central figure in this area. The talk will be self-contained, intended for an audience with different philosophical and technical interests.
Note: We will be having dinner right after the meeting at the Faculty House. Please let the rapporteur, Michael Nielsen (mn2683@columbia.edu), know if you would like to join us so that we can make the appropriate number of reservations (please be advised that at this point the university agrees to cover the expenses of the speaker and the rapporteur only and that the cost for all others is $30, payable by cash or check).
Title: A Mechanistic Conception of Metaphysical Grounding
Abstract: A dominant theoretical framework in philosophy of science employs the notion of mechanistic dependence to elucidate how higher-level, less fundamental phenomena depend upon and arise out of lower-level, more fundamental phenomena. To elucidate the same thing, literature in metaphysics employs the notion of grounding. As I argue, regardless of whether the notion of mechanistic dependence or the notion of grounding is used to theoretically portray how higher-level phenomena arise out of lower-level phenomena, what is captured by such portrayals is the same. Thus, these notions pick out the same features of the world. With this as my basis, I identify the notion of grounding with the notion of mechanistic dependence, and thus, construct a mechanistic conception of grounding. Since mechanistic dependence is understood in terms of mechanisms, my conception frames grounding in terms of mechanisms. Moreover, the contemporary notion of mechanisms is shaped by how mechanisms are represented via the mechanistic models and mechanistic explanations provided by science. Thus, because my conception grounding identifies grounding with mechanistic dependence and thereby frames grounding in terms of mechanisms, this conception suggests that the notion of grounding is to be tailored to and constrained by the mechanistic models and mechanistic explanations provided by science. This leads the mechanistic conception of grounding to reject a wide variety of conventional claims about grounding, and thus, to offer a treatment of grounding that is highly revisionary. To reinforce the plausibility of the mechanistic conception of grounding, I discuss how grounding and mechanistic dependence are associated with explanation. Whereas mechanistic dependence is associated with mechanistic explanation, grounding is associated with grounding explanation. For each kind of explanation, some higher-level phenomenon P is explained by appeal to some low-level phenomenon that Parises out of. As I argue, these forms of explanation can be plausibly identified. This greatly supports the mechanistic conception of grounding. For if grounding explanations employ the notion of grounding and mechanistic explanations employ the notion of mechanistic explanation, and these forms of explanation can be identified, this suggests that these explanations employ the same notion. And, just as the notions of grounding and mechanistic dependence capture the same connection between higher-level and lower-level phenomena, grounding explanation and mechanistic explanation do so as well. Finally, to argue that the mechanistic conception is to be preferred to standard conceptions, I argue that my conception offers a powerful defense of grounding from recent criticisms.
- - - - Tuesday, Apr 30, 2019 - - - -
- - - - Wednesday, May 1, 2019 - - - -
- - - - Thursday, May 2, 2019 - - - -
- - - - Friday, May 3, 2019 - - - -
Set Theory Seminar
CUNY Graduate Center, Room 6417
Friday, May 3, 10:00-11:45am
Joseph Van Name, CUNY Lower bounds on the cardinalities of quotient algebras of elementary embeddings
From non-trivial elementary embeddings j1…jr:Vλ→Vλj1…jr:Vλ→Vλ, we obtain a sequence of polynomials (pn(x1,…,xr))n∈ω(pn(x1,…,xr))n∈ω that satisfies the infinite product∞∏k=0pk(x1,…,xr)=11−(x1+⋯+xr).∏k=0∞pk(x1,…,xr)=11−(x1+⋯+xr).From this infinite product, we deduce lower bounds of the cardinality of |⟨j1,...,jr⟩/≡α||⟨j1,...,jr⟩/≡α| using analysis and analytic number theoretic techniques. Computer calculations that search for Laver-like algebras give some empirical evidence that these lower bounds cannot be greatly improved.
Model Theory Seminar
CUNY Graduate Center, Room 6417
Friday, May 3, 12:30-2:00pm
Artem Chernikov, UCLA
TBA
Logic Workshop
CUNY Graduate Center, Room 6417
Friday, May 3, 2:00-3:30pm
Gregory Cherlin, Rutgers University Countable universal graphs with forbidden subgraphs
Abstract
Definition: A collection FF of forbidden subgraphs is a Rado family if the class of countable FF-free graphs contains a universal structure with respect to embeddings as induced subgraphs. (By 'forbidden' I mean forbidden as subgraphs; usage varies in the literature.)
We consider the following decision problem for Rado families.
Problem: Given a finite set FF of finite, connected graphs, determine whether or not it is a Rado family.
Question: Is this a decidable problem?
If we specialize to the sake of a single constraint then we speak instead of a Rado constraint. Much is known, and much more conjectured, about the case of a single constraint.
Conjecture: The decision problem for the case of a single constraint is decidable.
Discussion
From the model theoretic side, a finite collection of forbidden subgraphs specifies a universal theory with some special properties: notably, there is a model companion. When we restrict to families of connected constraints, the theory has joint embedding and the model companion is complete. In model theoretic terms the question becomes whether the model companion has a countable universal model with respect to elementary embedding, for which a purely type theoretic criterion is known.
Decision problems for other model theoretic properties of the model companion are natural. We have focused on this one because the question came to us from graph theory. However, even in that form, two variants are relevant.
Can we decide whether the model companion is ℵ0ℵ0-categorical?
Dropping the connectedness hypothesis on the constraints, can we decide whether the model companion is complete?
The main source of positive answers to the universality problem appears to be the ℵ0ℵ0-categorical case, and this has some theoretical justification. The most direct route to understanding the original graph theoretical problem appears to take the detour through ℵ0ℵ0-categoricity.
As time allows, I would like to discuss the following three points.
What we know, and what we expect, in the case of a single constraint;
Methods of proof (algebraic closure; induction by pruning);
The status of the decision problem for j.e.p. and its analog in the theory of permutation pattern classes (work of Braunfeld).
This is joint work with Shelah, e.g. [Sh689].
- - - - Other Logic News - - - -
Conference announcement:
Model Theory and Mathematical Logic, in honor of Chris Laskowski's 60th birthday, June 21 - 23, 2019, at The University of Maryland, College Park http://www.umdlogic2019.com/
The 2019 Boise Extravaganza in Set Theory will take place in Ashland, Oregon, on the campus of Southern Oregon University, during June 19-21.
We are currently welcoming applications for travel grants from graduate students and postdocs (and other categories) in set theory and related fields. We will begin considering applications on May 1. We will continue accepting applications on a rolling basis until May 31.
Plenary speakers:
Dana Bartosova (University of Florida) Steve Jackson (University of North Texas) Reese Johnston (University of Washington Robinson Center) Assaf Shani (UCLA) Piotr Szeczwak (Cardinal Stefan Wyszyński University, Warsaw)
The BEST conference particularly aims to support the careers of young researchers in set theory (and related fields!), with travel support available for graduate students and postdocs. BEST features professional development opportunities and awards for student presentations. Please pass this invitation along to students, postdocs, and colleagues to submit an abstract and participate in BEST!
BEST is an international conference featuring talks on a broad range of recent advances in set theory research. The conference is organized by the Set Theory group at Boise State University and is structured as a symposium of the 100th annual meeting of the American Association for the Advancement of Science, Pacific Division (AAAS-PD). BEST is also supported by the NSF and Boise State University.
Organizers: Liljana Babinkostova (Boise State University), John Clemens (Boise State University), Samuel Coskey (Boise State University), Marion Scheepers (Boise State University). Scientific Committee: Natasha Dobrinen (University of Denver), Simon Thomas (Rutgers University)
Many thanks to Victoria Gitman for her development work!
-------- ADMINISTRIVIA --------
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Boise Extravaganza in Set Theory, second announcement
Conference
4/24/2019
The 2019 Boise Extravaganza in Set Theory will take place in Ashland, Oregon, on the campus of Southern Oregon University, during June 19-21.
We are currently welcoming applications for travel grants from graduate students and postdocs (and other categories) in set theory and related fields. We will begin considering applications on May 1. We will continue accepting applications on a rolling basis until May 31.
Plenary speakers:
Dana Bartosova (University of Florida)
Steve Jackson (University of North Texas)
Reese Johnston (University of Washington Robinson Center)
Assaf Shani (UCLA)
Piotr Szeczwak (Cardinal Stefan Wyszyński University, Warsaw)
Contact:
myself or best@boisestate.edu
**
The BEST conference particularly aims to support the careers of young researchers in set theory (and related fields!), with travel support available for graduate students and postdocs. BEST features professional development opportunities and awards for student presentations. Please pass this invitation along to students, postdocs, and colleagues to submit an abstract and participate in BEST!
BEST is an international conference featuring talks on a broad range of recent advances in set theory research. The conference is organized by the Set Theory group at Boise State University and is structured as a symposium of the 100th annual meeting of the American Association for the Advancement of Science, Pacific Division (AAAS-PD). BEST is also supported by the NSF and Boise State University.
Organizers: Liljana Babinkostova (Boise State University), John Clemens (Boise State University), Samuel Coskey (Boise State University), Marion Scheepers (Boise State University). Scientific Committee: Natasha Dobrinen (University of Denver), Simon Thomas (Rutgers University)
Tagged: Dana Bartošová, Steve Jackson, Reese Johnston, Assaf Shani, Piotr Szewczak
Fulgencio Lopez; Compact extensions of first order logic; cont.
IMPAN Working Group in Applications of Set Theory
4/23/2019
Seminar: Working group in applications of set theory, IMPAN
NOTE UNUSUAL TIME AND PLACE:
Friday, 26.04.2019, 10:15, room 106, IMPAN
Speaker: Fulgencio Lopez (IM PAN)
Title: "Compact extensions of first order logic" continuation from 16.04.
Abstact: "We aim to provide an exhaustive proof of the results of Keisler and Magidor and Malitz about the compactness of certain extensions of first order logic. Keisler's Theorem refers to the extension L(Q) where Q is the quantifier "There is an uncountable subset with a one dimensional property", similarly we can define Q_n to be "There is an uncountable subset with an n-dimensional property". We will show that L(Q) is compact (Keisler's Theorem) and, assuming diamond, so is L(Q_n:n∈ N) (Magidor and Malitz). We will also discuss why this framework can sometimes be useful for constructions of set theoretical structures".
Until May 9 the meetings of the seminar will take place at unusual times due to holidays and to the scientific Council of the Institute.
We go back to the usual Thursday time on May 9.
Visit our seminar page which may include some future talks at https://www.impan.pl/~set_theory/Seminar/
Tagged: Fulgencio Lopez
This Week in Logic at CUNY
This Week in Logic at CUNY
4/22/2019
Hi everyone,
I hope your Spring Break is going well. I'm sending out this special edition of "This Week in Logic" to announce this Wednesday's New York City Category Theory Seminar talk (and give a preview of next week's events).
All the best,
Jonas
This Week in Logic at CUNY:
- - - - Monday, Apr 22, 2019 - - - -
*** NOTE: CUNY Spring Break April 19-28 ***
- - - - Tuesday, Apr 23, 2019 - - - -
- - - - Wednesday, Apr 24, 2019 - - - -
The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York
Speaker: Andrei Rodin, Senior Researcher at the Institute of Philosophy of Russian Academy of Sciences.
Date and Time: Wednesday April 24, 2019, 7:00 - 8:30 PM., Room 6417.
Title: Directed Homotopy Type Theory and the (In)vertibility of Mathematics.
Abstract: Directed Homotopy Type theory (DHTT) is a generalization of Homotopy Type theory (HoTT) where fundamental groupoids of spaces are replaced by more general (higher) categories. Along with type formers for identity types which admit the standard HoTT interpretation in terms of invertible paths and their homotopies, DHTT comprises type formers for non-invertable homomorphisms of all levels which admit an interpreation in terms of non-invertable paths in appropriate spaces. The choice between DHTT and HoTT as foundational formal frameworks for building mathematical theories has an epistemological dimension, which concerns the epistemic significance of the invertibility condition. While HoTT and the related notion of Univalent Foundations support Mathematical Structuralism DHTT supports a more dynamic conception of Mathematics, which I shall outline in my talk.
Related papers:
Paige North, Towards a Directed Homotopy Type Theory, arXiv:1807.10566
Andrei Rodin, Categories Without Structures, arXiv: 0907.5143 (published in Philosophia Mathematica 19/1 (2011), p. 20-46)
Michael Warren, Directed Type Theory (video of talk in IAS Princeton)
- - - - Thursday, Apr 25, 2019 - - - -
- - - - Friday, Apr 26, 2019 - - - -
Next Week in Logic at CUNY:
- - - - Monday, Apr 29, 2019 - - - -
Logic and Metaphysics Workshop
Date: Monday, April 29th, 4.15-6.15
Place: Room 7314, CUNY Graduate Center
Speaker: Tommy Kivatinos (CUNY)
Title: A Mechanistic Conception of Metaphysical Grounding
Abstract: A dominant theoretical framework in philosophy of science employs the notion of mechanistic dependence to elucidate how higher-level, less fundamental phenomena depend upon and arise out of lower-level, more fundamental phenomena. To elucidate the same thing, literature in metaphysics employs the notion of grounding. As I argue, regardless of whether the notion of mechanistic dependence or the notion of grounding is used to theoretically portray how higher-level phenomena arise out of lower-level phenomena, what is captured by such portrayals is the same. Thus, these notions pick out the same features of the world. With this as my basis, I identify the notion of grounding with the notion of mechanistic dependence, and thus, construct a mechanistic conception of grounding. Since mechanistic dependence is understood in terms of mechanisms, my conception frames grounding in terms of mechanisms. Moreover, the contemporary notion of mechanisms is shaped by how mechanisms are represented via the mechanistic models and mechanistic explanations provided by science. Thus, because my conception grounding identifies grounding with mechanistic dependence and thereby frames grounding in terms of mechanisms, this conception suggests that the notion of grounding is to be tailored to and constrained by the mechanistic models and mechanistic explanations provided by science. This leads the mechanistic conception of grounding to reject a wide variety of conventional claims about grounding, and thus, to offer a treatment of grounding that is highly revisionary. To reinforce the plausibility of the mechanistic conception of grounding, I discuss how grounding and mechanistic dependence are associated with explanation. Whereas mechanistic dependence is associated with mechanistic explanation, grounding is associated with grounding explanation. For each kind of explanation, some higher-level phenomenon P is explained by appeal to some low-level phenomenon that Parises out of. As I argue, these forms of explanation can be plausibly identified. This greatly supports the mechanistic conception of grounding. For if grounding explanations employ the notion of grounding and mechanistic explanations employ the notion of mechanistic explanation, and these forms of explanation can be identified, this suggests that these explanations employ the same notion. And, just as the notions of grounding and mechanistic dependence capture the same connection between higher-level and lower-level phenomena, grounding explanation and mechanistic explanation do so as well. Finally, to argue that the mechanistic conception is to be preferred to standard conceptions, I argue that my conception offers a powerful defense of grounding from recent criticisms.
- - - - Tuesday, Apr 30, 2019 - - - -
- - - - Wednesday, May 1, 2019 - - - -
- - - - Thursday, May 2, 2019 - - - -
- - - - Friday, May 3, 2019 - - - -
Set Theory Seminar
CUNY Graduate Center, Room 6417
Friday, May 3, 10:00-11:45am
Joseph Van Name, CUNY Lower bounds on the cardinalities of quotient algebras of elementary embeddings
From non-trivial elementary embeddings j1…jr:Vλ→Vλj1…jr:Vλ→Vλ, we obtain a sequence of polynomials (pn(x1,…,xr))n∈ω(pn(x1,…,xr))n∈ω that satisfies the infinite product∞∏k=0pk(x1,…,xr)=11−(x1+⋯+xr).∏k=0∞pk(x1,…,xr)=11−(x1+⋯+xr).From this infinite product, we deduce lower bounds of the cardinality of |⟨j1,...,jr⟩/≡α||⟨j1,...,jr⟩/≡α| using analysis and analytic number theoretic techniques. Computer calculations that search for Laver-like algebras give some empirical evidence that these lower bounds cannot be greatly improved.
Model Theory Seminar
CUNY Graduate Center, Room 6417
Friday, May 3, 12:30-2:00pm
Artem Chernikov, UCLA
TBA
Logic Workshop
CUNY Graduate Center, Room 6417
Friday, May 3, 2:00-3:30pm
Gregory Cherlin, Rutgers University Countable universal graphs with forbidden subgraphs
Abstract
Definition: A collection FF of forbidden subgraphs is a Rado family if the class of countable FF-free graphs contains a universal structure with respect to embeddings as induced subgraphs. (By 'forbidden' I mean forbidden as subgraphs; usage varies in the literature.)
We consider the following decision problem for Rado families.
Problem: Given a finite set FF of finite, connected graphs, determine whether or not it is a Rado family.
Question: Is this a decidable problem?
If we specialize to the sake of a single constraint then we speak instead of a Rado constraint. Much is known, and much more conjectured, about the case of a single constraint.
Conjecture: The decision problem for the case of a single constraint is decidable.
Discussion
From the model theoretic side, a finite collection of forbidden subgraphs specifies a universal theory with some special properties: notably, there is a model companion. When we restrict to families of connected constraints, the theory has joint embedding and the model companion is complete. In model theoretic terms the question becomes whether the model companion has a countable universal model with respect to elementary embedding, for which a purely type theoretic criterion is known.
Decision problems for other model theoretic properties of the model companion are natural. We have focused on this one because the question came to us from graph theory. However, even in that form, two variants are relevant.
Can we decide whether the model companion is ℵ0ℵ0-categorical?
Dropping the connectedness hypothesis on the constraints, can we decide whether the model companion is complete?
The main source of positive answers to the universality problem appears to be the ℵ0ℵ0-categorical case, and this has some theoretical justification. The most direct route to understanding the original graph theoretical problem appears to take the detour through ℵ0ℵ0-categoricity.
As time allows, I would like to discuss the following three points.
What we know, and what we expect, in the case of a single constraint;
Methods of proof (algebraic closure; induction by pruning);
The status of the decision problem for j.e.p. and its analog in the theory of permutation pattern classes (work of Braunfeld).
This is joint work with Shelah, e.g. [Sh689].
- - - - Other Logic News - - - -
Conference announcement:
Model Theory and Mathematical Logic, in honor of Chris Laskowski's 60th birthday, June 21 - 23, 2019, at The University of Maryland, College Park http://www.umdlogic2019.com/
Many thanks to Victoria Gitman for her development work!
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Wednesday seminar
Prague Set Theory Seminar
4/18/2019
Dear all,
The seminar meets on Wednesday April 24th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
There is no fixed program yet. If nobody is willing to talk about
something, I may have a backup topic (probably reviewing some results
about forcing axioms and weak square principles).
Best,
David
Young Set Theory Workshop and European Set Theory Conference - early registration extended
Conference
4/17/2019
Dear All,
We have extended our early registration period till May 15 for both the Young Set Theory Workshop and the European Set Theory Conference. Please follow the links below and note that the registration is separate for the two meetings. There is limited financial support available for young researchers through the ASL and NSF; please see the websites.
Details: European Set Theory Conference
If you indicated to give a contributed lecture at the ESTC, please submit your abstract as soon as possible (you can use the code received at registration to edit your original registration and submit an abstract).
Details: Advanced Class 2019 (Young Set Theory Workshop)
Please upload a short research statement with your registration to the YSTW (or if you registered already, please add this statement using the code you received).
We are very much looking forward to seeing you in Vienna.
Heads up, CUNY Spring Break takes place starting this Friday, April 19-28. Regular mailings of "This Week in Logic" will resume on Sunday, April 28.
All the best,
Jonas
This Week in Logic at CUNY:
- - - - Monday, Apr 15, 2019 - - - -
Logic and Metaphysics Workshop
Date: Monday, April 15th, 4.15-6.15
Place: Room 7314, CUNY Graduate Center
Speaker: Jenn McDonald (CUNY)
Title: Structural Counterfactuals and the Importation Problem
Abstract: Structural causal models lend themselves to an analysis of counterfactuals – a structural semantics of counterfactuals. The basic idea is that a causal model allows for the clear and precise evaluation of any counterfactual encoded by it. Many argue that a structural semantics is superior to a more traditional similarity semantics, in part due to the latter’s independence from any notion of similarity(Galles & Pearl, 1998; Gallow, 2016; Hiddleston, 2005; Hitchcock, 2018; Pearl, 2000; Starr, 2019). I argue, though, that this is too quick. A similarity semantics employs the notion of similarity to answer what Priest (2018) calls the importation problem– the question of what information is to be held fixed in a counterfactual evaluation. I argue that where similarity semantics relies on an unarticulated notion of similarity, a structural semantics relies on an unarticulated notion of aptness. The superiority of structural semantics depends on its ability to deliver on a principled guide to determining which model(s) is apt. In this talk I go some way towards providing this guide.
- - - - Tuesday, Apr 16, 2019 - - - -
- - - - Wednesday, Apr 17, 2019 - - - -
The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York
Speaker: Tibor Beke, University of Massachusetts, Lowell.
Date and Time: Wednesday April 17, 2019, 7:00 - 8:30 PM., Room 6417.
Title: Schanuel functors and the Grothendieck (semi)ring of some theories.
Abstract: In a little known article, Schanuel defines a functor from semirings to idempotent semirings and a notion of dimension that is not linearly ordered. He uses it to give an elegant presentation of the Grothendieck semiring of semi-algebraic sets, from which the (much better known) structure of the Grothendieck ring of semi-algebraic sets easily follows. I will review his work and related results on the Grothendieck semiring of algebraically closed fields and similar geometric structures.
Fulgencio Lopez: Compact extensions of first order logic
IMPAN Working Group in Applications of Set Theory
4/12/2019
Seminar: Working group in applications of set theory, IMPAN
NOTE UNUSUAL TIME AND PLACE:
Tuesday, 16.04.2019, 10:15, room 106, IMPAN
Speaker: Fulgencio Lopez (IM PAN)
Title: "Compact extensions of first order logic"
Abstact: "We aim to provide an exhaustive proof of the results of Keisler and Magidor and Malitz about the compactness of certain extensions of first order logic. Keisler's Theorem refers to the extension L(Q) where Q is the quantifier "There is an uncountable subset with a one dimensional property", similarly we can define Q_n to be "There is an uncountable subset with an n-dimensional property". We will show that L(Q) is compact (Keisler's Theorem) and, assuming diamond, so is L(Q_n:n∈ N) (Magidor and Malitz). We will also discuss why this framework can sometimes be useful for constructions of set theoretical structures".
Until May 9 the meetings of the seminar will take place at unusual times due to holidays and to the scientific Council of the Institute
Visit our seminar page which may include some future talks at https://www.impan.pl/~set_theory/Seminar/
Tagged: Fulgencio Lopez
UPDATE: This Week in Logic at CUNY
This Week in Logic at CUNY
4/12/2019
Hi everyone,
This morning's Set Theory Seminar talk is cancelled, due to illness.
Regrets,
Jonas
This Week in Logic at CUNY:
- - - - Monday, Apr 8, 2019 - - - -
Logic and Metaphysics Workshop
Date: Monday, April 8th, 4.15-6.15
Place: Room 7314, CUNY Graduate Center
Speaker: Chris Scambler (NYU)
Title: Classical Logic and the Strict Tolerant Hierarchy
Abstract: In this talk I will do three things. First: I will present the central results from Barrio, Pailos and Szmuc’s recent paper “A hierarchy of classical and paraconsistent logics” (forthcoming in the JPL) along with some generalizations derived by observing certain symmetries; second, I will discuss the relation between the strict tolerant logics and classical logic, K3 and LP; third, I will try to convey the exact state of uncertainty about the philosophical significance of the foregoing I find myself in on the day.
- - - - Tuesday, Apr 9, 2019 - - - -
- - - - Wednesday, Apr 10, 2019 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center, Room 4213.03 (Math Thesis Room)
Wednesday, April 10, 6:30-8:00pm
Erez Shochat, St. Francis College
Introduction to Loeb Measure
In this talk we will outline results and facts from nonstandard analysis and introduce the concept of Loeb Measure.
- - - - Thursday, Apr 11, 2019 - - - -
- - - - Friday, Apr 12, 2019 - - - -
Set Theory Seminar
CUNY Graduate Center, Room 6417
Friday, April 12, 10:00-11:45am
Jonas Reitz, CUNY
Generalized Cohen Iterations
Adding Cohen subsets to each of a class of cardinals in turn is a common construction in set theory, and underlies many fundamental results. The construction comes in two basic flavors, products (as in Easton’s Theorem on the powers of regular cardinals) and iterations (forcing the GCH). These flavors are apparently quite similar, forcing at stage kappa to add subsets via the Cohen partial order Add(kappa,lambda). They differ only in the universe over which Add(kappa,lambda) is defined - in the case of products the ground model poset is used at each stage, whereas in typical iterations the poset is taken from the partial extension up to kappa. In this talk I will consider an alternative, in which we allow Add(kappa,lambda) to be defined over an arbitrary inner model (lying between the ground model and the extension up to kappa) at each stage. These generalized Cohen iterations are ZFC-preserving, although neither the proof for products nor for traditional iterations transfers directly. They allow constructions such as class iterations of class products of Cohen forcing, with applications including new work with Kameryn Williams on iterating the Mantle.
The logic Lω1ωLω1ω is obtained by closing finitary first-order logic under countable disjunction and conjunction. There is a kind of normal form for such sentences. For any structure AA there is a sentence of Lω1ωLω1ω, known as its Scott sentence, which describes AA up to isomorphism among countable structures. Given a countable scattered linear order LL of Hausdorff rank α<ω1α<ω1, we show that it has a dd-Σ2α+1Σ2α+1 Scott sentence. From Ash's calculation of the back and forth relations for all countable well-orders, we obtain that this upper bound is tight, i.e., for every α<ω1α<ω1 there is a linear order whose optimal Scott sentence has this complexity.
Logic Workshop
CUNY Graduate Center, Room 6417
Friday, April 12, 2:00-3:30pm
Julia Knight, University of Notre Dame Coding structures
A Turing computable embedding is a Turing operator that maps one class of structures to another so as to preserve isomorphism. The embedding codes the input structure in the output structure. It is interesting when there is an effective decoding. It is also interesting when the decoding is very difficult. Recently, Harrison-Trainor, Melnikov, R. Miller, and Montalbán have defined very general notions of interpretation, in which the interpreting formulas have no fixed arity. Uniformly defined interpretations give us decoding. I will discuss some known Turing computable embeddings, looking for uniform interpretations that yield effective, or Borel, decoding.
Marker's embedding of directed graphs in undirected graphs,
Mal'tsev's embedding of fields in groups,
Friedman and Stanley's embedding of graphs in linear orderings.
The first two embeddings come with uniform 'effective' interpretations, which give uniform effective decoding. For the third, we do not even have uniform interpretation via Lω1ωLω1ω formulas.
Next Week in Logic at CUNY:
- - - - Monday, Apr 15, 2019 - - - -
Logic and Metaphysics Workshop
Date: Monday, April 15th, 4.15-6.15
Place: Room 7314, CUNY Graduate Center
Speaker: Jenn McDonald (CUNY)
Title: Structural Counterfactuals and the Importation Problem
Abstract: Structural causal models lend themselves to an analysis of counterfactuals – a structural semantics of counterfactuals. The basic idea is that a causal model allows for the clear and precise evaluation of any counterfactual encoded by it. Many argue that a structural semantics is superior to a more traditional similarity semantics, in part due to the latter’s independence from any notion of similarity(Galles & Pearl, 1998; Gallow, 2016; Hiddleston, 2005; Hitchcock, 2018; Pearl, 2000; Starr, 2019). I argue, though, that this is too quick. A similarity semantics employs the notion of similarity to answer what Priest (2018) calls the importation problem– the question of what information is to be held fixed in a counterfactual evaluation. I argue that where similarity semantics relies on an unarticulated notion of similarity, a structural semantics relies on an unarticulated notion of aptness. The superiority of structural semantics depends on its ability to deliver on a principled guide to determining which model(s) is apt. In this talk I go some way towards providing this guide.
- - - - Tuesday, Apr 16, 2019 - - - -
- - - - Wednesday, Apr 17, 2019 - - - -
The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York
Speaker: Tibor Beke, University of Massachusetts, Lowell.
Date and Time: Wednesday April 17, 2019, 7:00 - 8:30 PM., Room 6417.
Title: Schanuel functors and the Grothendieck (semi)ring of some theories.
Abstract: In a little known article, Schanuel defines a functor from semirings to idempotent semirings and a notion of dimension that is not linearly ordered. He uses it to give an elegant presentation of the Grothendieck semiring of semi-algebraic sets, from which the (much better known) structure of the Grothendieck ring of semi-algebraic sets easily follows. I will review his work and related results on the Grothendieck semiring of algebraically closed fields and similar geometric structures.
Many thanks to Victoria Gitman for her development work!
-------- ADMINISTRIVIA --------
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Logic Seminar 17 April 2019 17:00 hrs at NUS
NUS Logic Seminar
4/11/2019
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 17 April 2019, 17:00 hrs
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Liu Tianyu
Title: Arithmetic algorithm of surreal numbers
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
The surreal number system is a totally ordered proper class
containing the real numbers as well as infinite and infinitesimal
numbers. A surreal number is sometimes defined as a function from an
initial segment of the ordinals into the set $(+,-)$, usually leads to
an infinite sign sequence. It can also be expressed uniquely in a
normal form, as $\sum_{i<\alpha} \omega^{a_i}r_i$.
In this talk I will present some algorithms for addition,
multiplication and division on the real field. Besides, we will cover
the normal form and sign sequence of surreal numbers, which will be
crucial for arithmetic algorithm of surreal numbers of length $>\omega$.
Ilijas Farah: Some necessary uses of set theory in mathematics
University of Vienna Mathematics Colloquium
4/10/2019
Mathematisches Kolloquium | 10.04.2019 16:15 - 19:00
Ilijas Farah (York University, Canada)
Abstract:
Every now and then, a difficult mathematical problem turns out to be difficult for a particularly objective reason: Provably, it cannot be solved by using `conventional' means. Some classical examples are proving the Continuum Hypothesis, duplicating the cube, and solving the quintic equation in radicals. I’ll discuss more recent examples of such problems, giving emphasis to those arising from the study of operator algebras.
William Chen: A Frechet space defined from a square principle
Toronto Set Theory Seminar
4/10/2019
Place: Fields Institute (Room 210)
Date: Friday 12, 2019 (13:30-15:00)
Speaker: William Chen
Title: A Frechet space defined from a square principle
Abstract: From $\Box(\kappa)$, we construct a Frechet $\alpha_1$-space
whose tightness in the topology obtained by declaring the $G_\delta$ sets
to be open is equal to $\kappa$. This complements the fact that under PFA,
every Frechet $\alpha_1$-space has tightness at most $\omega_1$ in the
$G_\delta$ modification. This space also satisfies several other
interesting properties from the theory of Frechet spaces.
(joint with P. Szeptycki)
Tagged: William Chen
Ralf Schindler: Variants of the extender algebra and their applications
Prague Set Theory Seminar
4/8/2019
Dear all,
There is no seminar this Wednesday.
The seminar meets again on Wednesday April 17th at 11:00 in the
Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front
building.
Program: Ralf Schindler -- Variants of the extender algebra and their
applications
Abstract. In the 1970’ies, Bukovský identified a beautiful and handy
criterion for when V is a forcing extension of a given inner model,
which proved very useful recently in set theoretical geology. In the
1990’ies, Woodin isolated his extender algebra which makes use of a
large cardinal, a Woodin cardinal. It turns out that Bukovský’s theorem
and Woodin’s extender algebra may be presented in a uniform fashion –
one proof and one forcing gives both results. We will discuss the proof
and applications in set theoretic and inner model theoretic geology and
then address (and answer) a question of T. Usuba on the \kappa-mantle.
In part, this is joint work with G. Sargsyan, F. Schlutzenberg, and my
student A. Lietz.
Best,
David
Tagged: Ralf Schindler
Re: Set Theory Seminar
Barcelona Set Theory Seminar
4/8/2019
Dear Colleagues,
Please find attached the announcement of the next session of the Barcelona Set Theory seminar.
Title: Classical Logic and the Strict Tolerant Hierarchy
Abstract: In this talk I will do three things. First: I will present the central results from Barrio, Pailos and Szmuc’s recent paper “A hierarchy of classical and paraconsistent logics” (forthcoming in the JPL) along with some generalizations derived by observing certain symmetries; second, I will discuss the relation between the strict tolerant logics and classical logic, K3 and LP; third, I will try to convey the exact state of uncertainty about the philosophical significance of the foregoing I find myself in on the day.
- - - - Tuesday, Apr 9, 2019 - - - -
- - - - Wednesday, Apr 10, 2019 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center, Room 4213.03 (Math Thesis Room)
Wednesday, April 10, 6:30-8:00pm
Erez Shochat, St. Francis College
Introduction to Loeb Measure
In this talk we will outline results and facts from nonstandard analysis and introduce the concept of Loeb Measure.
- - - - Thursday, Apr 11, 2019 - - - -
- - - - Friday, Apr 12, 2019 - - - -
Set Theory Seminar
CUNY Graduate Center, Room 6417
Friday, April 12, 10:00-11:45am
Jonas Reitz, CUNY
Generalized Cohen Iterations
Adding Cohen subsets to each of a class of cardinals in turn is a common construction in set theory, and underlies many fundamental results. The construction comes in two basic flavors, products (as in Easton’s Theorem on the powers of regular cardinals) and iterations (forcing the GCH). These flavors are apparently quite similar, forcing at stage kappa to add subsets via the Cohen partial order Add(kappa,lambda). They differ only in the universe over which Add(kappa,lambda) is defined - in the case of products the ground model poset is used at each stage, whereas in typical iterations the poset is taken from the partial extension up to kappa. In this talk I will consider an alternative, in which we allow Add(kappa,lambda) to be defined over an arbitrary inner model (lying between the ground model and the extension up to kappa) at each stage. These generalized Cohen iterations are ZFC-preserving, although neither the proof for products nor for traditional iterations transfers directly. They allow constructions such as class iterations of class products of Cohen forcing, with applications including new work with Kameryn Williams on iterating the Mantle.
The logic Lω1ωLω1ω is obtained by closing finitary first-order logic under countable disjunction and conjunction. There is a kind of normal form for such sentences. For any structure AA there is a sentence of Lω1ωLω1ω, known as its Scott sentence, which describes AA up to isomorphism among countable structures. Given a countable scattered linear order LL of Hausdorff rank α<ω1α<ω1, we show that it has a dd-Σ2α+1Σ2α+1 Scott sentence. From Ash's calculation of the back and forth relations for all countable well-orders, we obtain that this upper bound is tight, i.e., for every α<ω1α<ω1 there is a linear order whose optimal Scott sentence has this complexity.
Logic Workshop
CUNY Graduate Center, Room 6417
Friday, April 12, 2:00-3:30pm
Julia Knight, University of Notre Dame Coding structures
A Turing computable embedding is a Turing operator that maps one class of structures to another so as to preserve isomorphism. The embedding codes the input structure in the output structure. It is interesting when there is an effective decoding. It is also interesting when the decoding is very difficult. Recently, Harrison-Trainor, Melnikov, R. Miller, and Montalbán have defined very general notions of interpretation, in which the interpreting formulas have no fixed arity. Uniformly defined interpretations give us decoding. I will discuss some known Turing computable embeddings, looking for uniform interpretations that yield effective, or Borel, decoding.
Marker's embedding of directed graphs in undirected graphs,
Mal'tsev's embedding of fields in groups,
Friedman and Stanley's embedding of graphs in linear orderings.
The first two embeddings come with uniform 'effective' interpretations, which give uniform effective decoding. For the third, we do not even have uniform interpretation via Lω1ωLω1ω formulas.
Next Week in Logic at CUNY:
- - - - Monday, Apr 15, 2019 - - - -
Logic and Metaphysics Workshop
Date: Monday, April 15th, 4.15-6.15
Place: Room 7314, CUNY Graduate Center
Speaker: Jenn McDonald (CUNY)
Title: Structural Counterfactuals and the Importation Problem
Abstract: Structural causal models lend themselves to an analysis of counterfactuals – a structural semantics of counterfactuals. The basic idea is that a causal model allows for the clear and precise evaluation of any counterfactual encoded by it. Many argue that a structural semantics is superior to a more traditional similarity semantics, in part due to the latter’s independence from any notion of similarity(Galles & Pearl, 1998; Gallow, 2016; Hiddleston, 2005; Hitchcock, 2018; Pearl, 2000; Starr, 2019). I argue, though, that this is too quick. A similarity semantics employs the notion of similarity to answer what Priest (2018) calls the importation problem– the question of what information is to be held fixed in a counterfactual evaluation. I argue that where similarity semantics relies on an unarticulated notion of similarity, a structural semantics relies on an unarticulated notion of aptness. The superiority of structural semantics depends on its ability to deliver on a principled guide to determining which model(s) is apt. In this talk I go some way towards providing this guide.
- - - - Tuesday, Apr 16, 2019 - - - -
- - - - Wednesday, Apr 17, 2019 - - - -
The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York
Speaker: Tibor Beke, University of Massachusetts, Lowell.
Date and Time: Wednesday April 17, 2019, 7:00 - 8:30 PM., Room 6417.
Title: Schanuel functors and the Grothendieck (semi)ring of some theories.
Abstract: In a little known article, Schanuel defines a functor from semirings to idempotent semirings and a notion of dimension that is not linearly ordered. He uses it to give an elegant presentation of the Grothendieck semiring of semi-algebraic sets, from which the (much better known) structure of the Grothendieck ring of semi-algebraic sets easily follows. I will review his work and related results on the Grothendieck semiring of algebraically closed fields and similar geometric structures.
Many thanks to Victoria Gitman for her development work!
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
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Gao Ziyuan: Finitely distinguishable erasing pattern languages with bounded
variable frequency
NUS Logic Seminar
4/4/2019
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 10 April 2019, 17:00 hrs
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Gao Ziyuan
Title: Finitely distinguishable erasing pattern languages with bounded
variable frequency
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: A pattern is a nonempty string made up of symbols from two
disjoint sets, an alphabet $\Sigma$ of constant symbols and a
countably infinite set $X$ of variables. The erasing pattern
language $L(\pi)$ generated by a pattern $\pi$ is the set of all words
over $\Sigma$ obtained by replacing all the variables of $\pi$ with
arbitrary words over $\Sigma$, with the proviso that identical
variables be replaced with the same string. In particular,
patterns allow for repetitions of variable substrings, a feature known
as backreferencing in programming languages. A distinguishing
set for any pattern $\pi$ w.r.t. a class $\Pi$ of patterns containing
$\pi$ is a set $D$ of words over $\Sigma$ that distinguishes $\pi$
from every other pattern $\tau$ in $\Pi$ with $L(\tau) \neq L(\pi)$
(i.e., $D \cap L(\pi) \neq D \cap L(\tau)$ whenever $L(\tau) \neq
L(\pi)$).
Two basic types of counting problems will be discussed: first, given
any pattern $\pi$ belonging to a class $\Pi$ of patterns, does $\pi$
have a finite distinguishing set w.r.t. $\Pi$; second, what is the
minimum size of a distinguishing set for $\pi$ w.r.t. $\Pi$?
The latter quantity gives a measure of the information complexity of
$\pi$ w.r.t. $\Pi$, and it is known as the (classical) teaching
dimension of $\pi$ w.r.t. $\Pi$ in computational learning theory.
We also consider the problem of determining, for any given strict
partial order $\prec$ on $\Pi$ (up to equivalence of patterns) and any
pattern $\pi$ belonging to $\Pi$, the minimum size of a distinguishing
set for $\pi$ w.r.t. the subclass of all $\tau$ in $\Pi$ such that
$\tau \not\prec \pi$; this quantity is known as the preference-based
teaching dimension of $\pi$ w.r.t. $(\Pi,\prec)$. We study
how the classical and preference-based teaching dimensions of patterns
w.r.t. various "naturally" defined classes of patterns and strict
partial orders depend on the alphabet size and the maximum number of
variable repetitions in any single pattern belonging to the class.
Szymon Żeberski: Mycielski theorem and Miller trees
Wrocław University of Technology
4/3/2019
Tuesday, April 9, 2019, 17:15
Wrocław University of Technology, 215 D-1
Speaker: Szymon Żeberski (Wrocław University of Technology,)
Title: Mycielski theorem and Miller trees
Abstract:
The classical Mycielski theorem says that for comeager $A\subseteq [0,1]^2$ one can find a perfect set $P$ such that $P\times P\subseteq A\cup\Delta$. (The same is true if we start with $A$ of measure 1.)
We will discuss how far this can be generalized if we replace perfect set by superperfect set, i.e a body of a Miller tree.
It turns out that there is a comeager $A\subseteq (\omega^\omega)^2$ such that $A\cup \Delta$ does not contain any set of the form $M\times M$, where $M$ is superperfect.
However, for comeager $A\subseteq [0,1]^2$ one can find a perfect set $P$ and a superperfect set $M\supseteq P$ such that $P\times M\subseteq A\cup\Delta$.
We will also discuss measure case, where results are slightly different.
Tagged: Szymon Zeberski
Diana Carolina Montoya - The equality $\mathfrak{p} = \mathfrak{t}$ and the generalized characteristics
Kurt Godel Research Center
4/2/2019
Talk held by Diana Carolina Montoya (KGRC) at the KGRC seminar on 2019-04-04.
Abstract: Malliaris and Shelah solved in the positive the longstanding problem of whether the two cardinal invariants $\mathfrak{p}$ (the pseudointersection number) and $\mathfrak{t}$ (the tower number) are equal. In this talk, I will review some essential points in their proof in order to motivate the study of the analogous question for the generalized characteristics $\mathfrak{p}(\kappa)$ and $\mathfrak{t}(\kappa)$. I will present some results of Garti regarding this generalization and finally some recent progress (joint work with Fischer, Schilhan, and Soukup) towards answering this question.
Tagged: Diana Carolina Montoya
Wu Guohua: wtt-=degrees of dre sets
NUS Logic Seminar
4/1/2019
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 3 April 2019, 17:00 hrs
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Wu Guohua
Title: wtt-=degrees of dre sets
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: In this talk, I will present some recent work on wtt-degrees
of dre set. In particular, I will give a rough idea of showing the density
of this structure. I will also give a few projects in this direction.
Dorottya Sziraki: Open graphs and hypergraphs on definable subsets of generalized Baire spaces
Bristol Logic Seminar
4/1/2019
Tuesday, April 2, 2019, 15.00
Howard House 4th Floor Seminar Room, University of Bristol
Speaker: Dorottya Sziraki (Central European University, Budapest)
Title: Open graphs and hypergraphs on definable subsets of generalized Baire spaces
Abstract:
The open graph dichotomy for a given subset $X$ of the Baire space $\omega^\omega$ is a generalization of the perfect set property for $X$ which can be viewed as the perfect set version of the Open Coloring axiom restricted to $X$. In joint work with P. Schlicht, we extend a theorem of Q. Feng's about the open graph dichotomy for definable subsets of the Baire space to the generalized Baire space $\kappa^\kappa$, where $\kappa$ is any uncountable cardinal with $\kappa^{<\kappa}=\kappa$. More concretely, we show that the $\kappa$-analogue of the open graph dichotomy for all subsets of $\kappa^\kappa$ which are definable from a $\kappa$-sequence of ordinals is consistent relative to the existence of an inaccessible cardinal above $\kappa$. In the talk, I will sketch a proof of this result.
If time allows, I will also report on the progress of possible generalizations of Q. Feng's and our above mentioned theorems for certain definable infinite dimensional hypergraphs. These concern (special cases of) an infinite dimensional version of the open graph dichotomy which was recently introduced by R. Carroy, B.D. Miller and D.T. Soukup.
Tagged: Dorottya Sziráki
cmu math logic seminar, coming attractions
Carnegie Mellon Logic Seminar
4/1/2019
April 2 --- No seminar
April 9 --- Vahagn Aslanyan
April 16 --- Garrett Ervin
This Week in Logic at CUNY
This Week in Logic at CUNY
3/31/2019
This Week in Logic at CUNY:
- - - - Monday, Apr 1, 2019 - - - -
Logic and Metaphysics Workshop
Date: Monday, April 1st, 4.15-6.15
Place: Room 7314, CUNY Graduate Center
Speaker: Elena Ficara (Paderborn)
Title: What does it mean that Contradiction is the Norm of Truth?
Abstract: In my talk I argue for the thesis CT: contradiction is the norm of truth, and ask about its relevance for contemporary philosophical logic. I first present three positions in the history of philosophy that have advocated some versions of CT, namely Plato’s idea of the “dialectical gymnastics” in the Parmenides (Plato, Parmenides 136 B-E), Aristotle’s notion of dialectics in the Topics (Aristotle, Topics I, 2-3) and Metaphysics (Aristotle, Met III 1, 995 a 24-29), and Hegel’s contradictio est regula veri (Hegel Werke 2, 533), then derive from them some answers to the questions:
What is meant by “contradiction” in CT?
What is meant by “truth” in CT?
What is meant by “norm” in CT?
I will show that to examine the meaning of CT in historical perspective is useful to understand the seeds of genuine glut theories.
- - - - Tuesday, Apr 2, 2019 - - - -
- - - - Wednesday, Apr 3, 2019 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center, Room 4213.03 (Math Thesis Room)
Wednesday, April 3, 6:30-8:00pm
Michał Tomasz Godziszewski, University of Warsaw Π01Π10-computable quotient presentations of nonstandard models of arithmetic
A computable quotient presentation of a mathematical structure AA consists of a computable structure on the natural numbers ⟨N,⋆,∗,…⟩⟨N,⋆,∗,…⟩, meaning that the operations and relations of the structure are computable, and an equivalence relation EE on NN, not necessarily computable but which is a congruence with respect to this structure, such that the quotient ⟨N,⋆,∗,…⟩⟨N,⋆,∗,…⟩ is isomorphic to the given structure AA. Thus, one may consider computable quotient presentations of graphs, groups, orders, rings and so on.
A natural question asked by B. Khoussainov in 2016, is if the Tennenbaum Thoerem extends to the context of computable presentations of nonstandard models of arithmetic. In a joint work with J.D. Hamkins we have proved that no nonstandard model of arithmetic admits a computable quotient presentation by a computably enumerable equivalence relation on the natural numbers.
However, as it happens, there exists a nonstandard model of arithmetic admitting a computable quotient presentation by a co-c.e. equivalence relation. Actually, there are infinitely many of those. The idea of the proof consists in simulating the Henkin construction via finite injury priority argument. What is quite surprising, the construction works (i.e. injury lemma holds) by Hilbert's Basis Theorem. During the talk I'll present ideas of the proof of the latter result, which is joint work with T. Slaman and L. Harington.
The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
Date and Time: Wednesday April 3, 2019, 7:45 - 9:00 PM., Room 6417. (NOTICE SPECIAL TIME.)
Speaker: Eoin Moore, The Graduate Center, CUNY.
Title: The Arithmetical Completeness and Soundness of the Logic of Proofs.
Abstract: BHK semantics were introduced to provide a semantics of intuitionistic logic (Int) whereby the truth of a proposition was demonstrated by exhibiting a proof of it. This semi-rigorous approach had some serious difficulties with its exact formalization. The major hurdle of formalization was completed with Artemov's Logic of Proofs (LP), which provided the desired provability semantics. Int was embedded into LP, which was then embedded into Peano Arithmetic (PA). In this talk I will discuss the second inclusion. I will show that there is a complete and sound interpretation of LP into PA, in which LP proof terms are mapped to PA provability formulas.
- - - - Thursday, Apr 4, 2019 - - - -
- - - - Friday, Apr 5, 2019 - - - -
Set Theory Seminar
CUNY Graduate Center, Room 6417
Friday, April 5, 10:00-11:45am
Michał Tomasz Godziszewski, University of Warsaw
Set-Theoretic Independence and Machine Learning
In a recent exciting paper Learnability can be undecidable by S. Ben-David et. al. published in Nature Machine Intelligence the authors argue that certain abstract learnability questions are undecidable by ZFC axioms. The general learning problem considered there is to find a way of choosing a finite set that maximizes a particular expected value (within a certain range of error) with an obstacle that the probability distribution is unknown, or more formally: given a family of functions FF from some fixed domain XX to the real numbers and an unknown probability distribution μμ over XX, find, based on a finite sample generated by μμ, a function in FFwhose expectation with respect to μμ is (close to) maximal.
The authors then provide a translation from this statistical framework to infinite comibnatorics: namely, they prove that existence of certain learning functions corresponding to the problem above (the so-called estimating the maximum learners, or EMX-learners) translates into the existence of the so-called monotone compression schemes, which in turn is equivalent to a statement in cardinal arithmetic that is indeed independent of ZFC. Specifically, let XX be an infinite set, Fin(X)Fin(X) be the family of its finite subsets, and let m>km>k be natural nubers. A monotone compressions scheme for (X,m,k)(X,m,k) is a function f:[X]k→Fin(X)f:[X]k→Fin(X) such that∀A∈[X]m∃B∈[X]k(B⊆A⊆f(B)).∀A∈[X]m∃B∈[X]k(B⊆A⊆f(B)).
The main result of the paper then is that there exists a monotone compressions scheme for ([0,1],m+1,m)([0,1],m+1,m) for some mm if and only if 2ℵ0<ℵω2ℵ0<ℵω.
K.P. Hart immediately observed that the main combinatorial content of the results in the paper is related to Kuratowski's theorem on decompositions of finite powers of sets and that the monotone compression functions on the unit interval cannot, in a certain sense, be constructive or descriptively nice - namely, they cannot be Borel measurable. During the talk I will introduce the subject of the paper in question, and present the set-theoretic aspects of the main results.
Model companions of theories of valued differential fields
I will survey what is known about model companions of theories of (ordered) valued differential fields and discuss my ongoing work towards isolating a model companion for a certain theory of ordered valued differential fields, including positive results at the level of the value group.
Logic Workshop
CUNY Graduate Center, Room 6417
Friday, April 5, 2:00-3:30pm
Peter Cholak, University of Notre Dame Computability-Theoretic Aspects of Ramsey's Theorem
Ramsey's Theorem for pairs and 2 colors says that for every 2-coloring, CC, of pairs of natural numbers, there is an infinite set HH, such that all pairs from HH have the same constant color. HH is called a homogeneous set for CC. We will also consider Ramsey's Theorem in other settings. For example, we can be given countably many 11-colorings of natural numbers, {ci}{ci}, and ask for a set CCsuch that, for each ii, all but finitely many elements of CC have the same color with respect to cici. Call CC a cohesive set for {ci}{ci}. Among the questions we will explore here is what can be computed from homogeneous sets. For example, given countably many 11-colorings {ci}{ci}, is there a 2-coloring CC, such that every homogeneous set for CC computes a cohesive set for {ci}{ci}?
Next Week in Logic at CUNY:
- - - - Monday, Apr 8, 2019 - - - -
- - - - Tuesday, Apr 9, 2019 - - - -
- - - - Wednesday, Apr 10, 2019 - - - -
- - - - Thursday, Apr 11, 2019 - - - -
- - - - Friday, Apr 12, 2019 - - - -
Set Theory Seminar
CUNY Graduate Center, Room 6417
Friday, April 12, 10:00-11:45am
Jonas Reitz, CUNY
Generalized Cohen Iterations
Adding Cohen subsets to each of a class of cardinals in turn is a common construction in set theory, and underlies many fundamental results. The construction comes in two basic flavors, products (as in Easton’s Theorem on the powers of regular cardinals) and iterations (forcing the GCH). These flavors are apparently quite similar, forcing at stage kappa to add subsets via the Cohen partial order Add(kappa,lambda). They differ only in the universe over which Add(kappa,lambda) is defined - in the case of products the ground model poset is used at each stage, whereas in typical iterations the poset is taken from the partial extension up to kappa. In this talk I will consider an alternative, in which we allow Add(kappa,lambda) to be defined over an arbitrary inner model (lying between the ground model and the extension up to kappa) at each stage. These generalized Cohen iterations are ZFC-preserving, although neither the proof for products nor for traditional iterations transfers directly. They allow constructions such as class iterations of class products of Cohen forcing, with applications including new work with Kameryn Williams on iterating the Mantle.
Julia Knight, University of Notre Dame Coding structures
A Turing computable embedding is a Turing operator that maps one class of structures to another so as to preserve isomorphism. The embedding codes the input structure in the output structure. It is interesting when there is an effective decoding. It is also interesting when the decoding is very difficult. Recently, Harrison-Trainor, Melnikov, R. Miller, and Montalbán have defined very general notions of interpretation, in which the interpreting formulas have no fixed arity. Uniformly defined interpretations give us decoding. I will discuss some known Turing computable embeddings, looking for uniform interpretations that yield effective, or Borel, decoding.
Marker's embedding of directed graphs in undirected graphs,
Mal'tsev's embedding of fields in groups,
Friedman and Stanley's embedding of graphs in linear orderings.
The first two embeddings come with uniform 'effective' interpretations, which give uniform effective decoding. For the third, we do not even have uniform interpretation via Lω1ωLω1ω formulas.
Many thanks to Victoria Gitman for her development work!
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Joan Bagaria: Finite trees and stationary sets
Barcelona Set Theory Seminar
3/29/2019
Date: Thursday 4 April 2019
Time: 16:00
Place: Room S-1*
BARCELONA RESEARCH GROUP IN SET THEORY
BARCELONA SET THEORY SEMINAR
Title: Finite trees and stationary sets
Speaker: Joan Bagaria
Abstract: We shall present a proof of Andreas Blass’ embedding
theorem for finite rooted trees, which assigns pairwise-disjoint
stationary-reflecting sets of ordinals to the nodes of such a tree
in a coherent way. The proof uses Jensen’s square principle.
After identifying the main obstacles for the theorem’s
generalization to hyperstationary sets, we will show how one of
the obstacles may be removed by the use of the new notion of
hypercofinality.
Tagged: Joan Bagaria
Asger Törnquist: All about mad families
Israeli Logic Talks
3/28/2019
BIU Infinite Combinatorics Seminar
Mon, 01/04/2019 - 13:00
Speaker: Asger Törnquist
Title: All about mad families
Abstract. I will give an overview of the developments in the past 5 years regarding mad families.
We'll study families of subsets of the natural numbers, and say that such a family is almost disjoint if any two distinct elements intersect finitely. The Axiom of Choice implies the existence of infinite almost disjoint family which is maximal under inclusion.
Mathias proved in the late 1960s that it is consistent with ZF+DC that there are no mad families. He needed a Mahlo cardinal to do this. In 2014 I showed that the classical Solovay-Lévy model has no infinite mad families, and shortly thereafter, in 2016, Horowitz and Shelah showed that you don't even need an inaccessible to get a model of ZF+DC+no infinite mad families.
A wealth of related questions have also been settled, most recently, I have shown with David Schrittesser that "All sets are Ramsey"+"Ramsey uniformization" implies "no infinite mad families ".
I'll also discuss open problems. The talk will not assume any prior knowledge of mad families.
Tagged: Asger Tornquist
Egbert Thümmel: Topologies on Boolean algebras
Prague Set Theory Seminar
3/28/2019
Dear all,
The seminar meets on Wednesday April 3rd at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Egbert Thümmel -- Topologies on Boolean algebras
We define the sequential topology on complete Boolean algebra which was
successfully applied especially for ccc and Maharam algebras. B. Balcar
asked whether in this topology zero has always a neighbourhood base of
downward closed sets.
We give a precise answer to this question (equivalence in forcing terms)
and connections to other problems.
Best,
David
Tagged: Egbert Thümmel
Miha Habič: Capturing by normal ultrapowers
Kurt Godel Research Center
3/28/2019
Talk held by Miha Habič (Czech Technical University in Prague, Czech Republic and Charles University, Prague, Czech Republic) at the KGRC seminar on 2019-03-28.
Abstract: If $\kappa$ is measurable and GCH holds, then any ultrapower by a normal measure on $\kappa$ will be missing some subset of $\kappa^+$. On the other hand, Cummings showed that, starting from a $(\kappa+2)$-strong $\kappa$, one can force to a model (without collapsing cardinals) where $\kappa$ carries a normal measure whose ultrapower captures the entire powerset of $\kappa^+$. Moreover, the large cardinal hypothesis is optimal. I will present an improvement of Cummings' result and show that this capturing property can consistently hold at the least measurable cardinal.
This is joint work with Radek Honzík.
Tagged: Miha Habic
Logic Colloquium 2019 (reminder)
Conference
3/26/2019
This is a reminder that the deadline for early bird registrations for the Logic Colloquium 2019, August 11-16, Prague, Czech Republic is approaching.
Deadlines
Abstract submission April 30, 2019
Application for support April 15, 2019
Early bird registration May 15, 2019
The conference now has a website with more info, registration and abstract submission
Tagged: Andy Zucker, Daniel Soukup, Dilip Raghavan, Heike Mildenberger, Yair Hayut
Slawomir Solecki: Transfinite sequences of topologies and descriptive complexity
Toronto Set Theory Seminar
3/26/2019
Place: Fields Institute (Room 210)
Date: March 39, 2019 (13:30-15:00)
Speaker: Slawomir Solecki
Title: Transfinite sequences of topologies and descriptive complexity
Abstract: We introduce a notion of filtration from one topology $\sigma$ to another $\tau$ assuming that $\tau$ contains $\sigma$. Such filtrations are certain transfinite sequence of topologies interpolating between $\sigma$ and $\tau$. We consider the question of whether a filtration succeeds in reaching $\tau$, and, if it does, at what stage it happens. Answers to these questions involve descriptive set theoretic conditions on the relationship between $\sigma$ and $\tau$. This theme arose in investigations concerning the Scott analysis of certain definable equivalence relations, but the talk will be independent of these considerations.
Tagged: Slawomir Solecki
Ralf Schindler: Paradoxical" sets with no well-ordering of the reals"
Israeli Logic Talks
3/23/2019
HUJI Set Theory Seminar
On Wednesday, March 27, (14:00-15:30 in Ross 63) Ralf Schindler (Münster) will talk about "Paradoxical" sets with no well-ordering of the reals.
Abstract: By a Hamel basis we mean a basis for the reals, R, construed as a vecor space over the field of rationals. In 1905, G. Hamel constructed such a basis from a well-ordering of R. In 1975, D. Pincus and K. Prikry asked "whether a Hamel basis exists in any model in which R cannot be well ordered." About two years ago, we answered this positively in a joint paper with M. Beriashvili, L. Wu, and L. Yu. In more recent joint work, additionally with J. Brendle and F. Castiblanco we constructed a model of ZF with a Luzin set, a Sierpiński set, a Burstin basis, and a Mazurkiewicz set, but with no well-ordering of R. In joint work with V. Kanovei, we constructed such a model in which even all those "paradoxical" sets are projective.
Tagged: Ralf Schindler
Moritz Müller: Provability and consistency of circuit lower bounds
Barcelona Set Theory Seminar
3/22/2019
Date: Thursday 28 March 2019
Time: 16:00
Place: Room S-1*
Departament de Matemàtiques i Informàtica
Universitat de Barcelona
Gran Via de les Corts Catalanes 585, 08007 Barcelona
BARCELONA RESEARCH GROUP IN SET THEORY
BARCELONA SET THEORY SEMINAR
Speaker: Moritz Müller (UPC)
Title: Provability and consistency of circuit lower bounds
Abstract. In 1995 Razborov asked for the right fragment of
bounded arithmetic capturing existing techniques to prove
circuit lower bounds for explicit Boolean functions. The talk
reports some new developments.
Tagged: Moritz Müller
Damian Sobota: Josefson-Nissenzweig theorem for $C(K)$-spaces
Wrocław University of Technology
3/22/2019
Tuesday, March 26, 2019, 17:15
Wrocław University of Technology, 215 D-1
Speaker: Damian Sobota (Universityof Viena)
Title: Josefson-Nissenzweig theorem for $C(K)$-spaces
Abstract:
The Josefson-Nissenzweig theorem is a powerful tool in Banach space theory. Its special version for Banach spaces of continuous functions reads as follows: for a given infinite compact space K there exists a sequence $(\mu_n)$ of normalized signed Radon measures on K such that the integrals $\mu_n(f)$ converge to $0$ for any function $f$ in $C(K)$. During my talk I will investigate when the sequence $(\mu_n)$ can be chosen in such a way that every $\mu_n$ is just a finite linear combination of Dirac point measures (in other words, $\mu_n$ has finite support). This will appear to have connections with the Grothendieck property of Banach spaces and complementability of the space $c_0$. In particular, I'll present a very elementary proof that $c_0$ is always complemented in a space $C(K\times K)$.
Tagged: Damian Sobota
Saeed Ghasemi: AF-algebras with Cantor-set property
Prague Set Theory Seminar
3/20/2019
Dear all,
The seminar meets on Wednesday March 27th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Saeed Ghasemi -- AF-algebras with Cantor-set property
A separable AF-algebra is a C*-algebra which is (isomorphic to) the
inductive limit of a direct sequence of finite dimensional C*-algebras.
We introduce a class of separable AF-algebras, called AF-algebras with
Cantor-set property, which are, in some contexts, suitable
noncommutative analogues of the Cantor set. One of the main features of
AF-algebras with Cantor-set property is that they are all Fraisse
limits of some category of finite dimensional C*-algebras and left
invertible embeddings. As a consequence of this, many properties of the
Cantor set that can be proved using the Fraisse theory, such as the
homogeneity and universality, also can also be proved for AF-algebras
with Cantor-set property. In fact, the category of all finite
dimensional C*-algebras and left invertible embeddings is a Fraisse
category and its Fraisse limit is a separable AF-algebra with Cantor-set
property which has the universality property that maps surjectively onto
any separable AF-algebra.*
This is a joint work with Wieslaw Kubis.
*- All of these results can be restated and proved in the language of
partially ordered abelian groups without mentioning any C*-algebras.
Best,
David
Tagged: Saeed Ghasemi
Ashutosh Kumar: Order dimension of Turing degrees
NUS Logic Seminar
3/20/2019
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 27 March 2019, 17:00 hrs
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Ashutosh Kumar
Title: Order dimension of Turing degrees
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
The order dimension of a partially ordered set (P,<)
is the smallest size of a family F of linear orders,
each extending <, such that the intersection of F is
the given ordering <.
Higuchi, Lempp, Raghavan and Stephan asked if the order dimension
of Turing degrees could be decided in ZFC. We show that the answer is no.
This is joint work with Dilip Raghavan.
Tagged: Ashutosh Kumar
Spencer Unger: Stationary reflection and the singular cardinals hypothesis
Israeli Logic Talks
3/19/2019
HUJI Logic Seminar
Tomorrow, Spencer Unger will speak in our logic seminar about Stationary reflection and the singular cardinals hypothesis. As usual we meet at 11am in Ross 63. Looking forward to seeing you there,
Title: Stationary reflection and the singular cardinals hypothesis.
Abstact. We examine reflection of stationary sets at successors of singular cardinals and its connection with cardinal arithmetic. For instance it has been open whether the failure of the singular cardinal hypothesis at a singular cardinal mu of uncountable cofinality implies the existence of a nonreflecting stationary subset of mu^+. In recent joint work with Omer Ben-Neria and Yair Hayut we have shown that the answer is no modulo the consistency of some large cardinals. In this talk, we survey some instances of methods used in the proof. In particular, we show how to construct Prikry sequences over iterated ultrapowers and exploit them for combinatorial proofs.
Tagged: Spencer Unger
Ralf Schindler: Variants of the extender algebra and their applications
Israeli Logic Talks
3/19/2019
BIU Infinite Combinatorics Seminar
Mon, 25/03/2019 - 13:00
Speaker: Ralf Schindler (Münster)
Title: Variants of the extender algebra and their applications
Abstract. In the 1970'ies, Bukowský identified a beautiful and handy criterion for when V is a forcing extension of a given inner model, which proved very useful recently in set theoretical geology. In the 1990'ies, Woodin isolated his extender algebra which makes use of a large cardinal, a Woodin cardinal. It turns out that Bukowský's theorem and Woodin's extender algebra may be presented in a uniform fashion - one proof and one forcing gives both results. We will present the proof and then discuss its application in inner model theoretic geology. This is joint work with Grigor Sargsyan and Farmer Schlutzenberg.
Tagged: Ralf Schindler
Antonio Aviles: Twisted sums of spaces of continuous functions
Toronto Set Theory Seminar
3/19/2019
Place: Fields Institute (Room 210)
Date: March 22, 2019 (13:30-15:00)
Speaker: Antonio Aviles
Title: Twisted sums of spaces of continuous functions
Abstract: Given two Banach spaces $Z$ and $X$, can we find a Banach space $Y$ that contains $X$ as an uncomplemented subspace and $Y/X = Z$? We will mention two instances of this problem connected to set theoretic questions. When $X = c_0$ and $Z=C(K)$ is a space of continuous functions on a nonmetric compactum, the answer may be negative under $MA_{\omega_1}$ but it is always positive under CH (joint work with W. Marciszewski and G. Plebanek). When $X = \ell_\infty/c_0$ and $Z=c_0(\mathfrak{c})$, the answer is positive provided splitting chains exist in $\mathcal{P}(\omega)/fin$ (joint work with P. Borodulin-Nadzieja, F. Cabello, D. Chodounsk\'{y} and O. Guzm\'{a}n)
Tagged: Antonio Avilés
Yair Hayut: Strong compactness and the filter extension property
Kurt Godel Research Center
3/18/2019
Talk held by Yair Hayut (KGRC) at the KGRC seminar on 2019-03-21.
Abstract
The notion of strongly compact cardinal is one of the earliest large cardinal axioms, yet it is still poorly understood.
I will review some classical and semi-classical connections between partial strong compactness, the strong tree property and the filter extension property, getting a level-by-level equivalence and an elementary embedding characterization.
This analysis is especially interesting for the property "every κκ-complete filter on $\kappa$ can be extended to a $\kappa$ -complete ultrafilter" (where $\kappa$ is uncountable). This property was isolated by Mitchell and was named "$\kappa$ -compactness" by Gitik. In his recent paper, Gitik showed that some definable versions of it have a relatively low consistency strength, yet others provide an inner models with a Woodin cardinal. Applying the equivalence above to this case, I will improve the previously known lower bound for $\kappa$ -compactness.
Then, I'll move to a more speculative area, and conjecture that $\kappa$ -compactness is equiconsistent with a certain large cardinal axiom in the realm of subcompact cardinals. I will give a few arguments in favour of this conjecture.
Tagged: Yair Hayut
European Set Theory Conference 2019 - registration reminder
Kurt Godel Research Center
3/18/2019
Let us remind you that registration is open (still with the Early Fee) for the European Set Theory Conference. We welcome contributed talks and encourage you to take advantage of the support from ASL.
Details: European Set Theory Conference
Please note that the registration for the Advanced Class 2019 (Young Set Theory Workshop) is separate.
Advanced Class 2019 (Young Set Theory Workshop) - registration reminder
Conference
3/18/2019
Let us remind you that registration is open (still with the Early Fee) for the Advanced Class 2019 (Young Set Theory Workshop). We welcome poster submissions and encourage you to take advantage of the support from ASL.
Details: Advanced Class 2019 (Young Set Theory Workshop)
Please note that the registration for the European Set Theory Conference is separate.
Jing Zhang: Poset dimension and singular cardinals
Carnegie Mellon Logic Seminar
3/15/2019
Mathematical logic seminar - Mar 19 2019
Time: 3:30pm - 4:30 pm
Room: Wean Hall 8220
Speaker: Jing Zhang
CMU
Title: Poset dimension and singular cardinals
Abstract:
The dimension of a poset (P, ≤P) is defined as the least cardinal λ such that there exists a λ-sized collection of linear extensions of P realizing P, that is to say a ≤P b if and only a ≤ b in any linear extension in the collection. We will focus on the poset Pα(κ), that is the poset of subsets of κ of size less than α partially ordered by inclusion, and determine completely the dimension of such posets under GCH. Then we will mention a few consistency results when GCH fails. In particular, we point out the connection between the dimension of the poset Pα (2κ) and the density of 2κ under the <α-box product topology, and show it is consistent that they are different.
Tagged: Jing Zhang
Samuel Gomes da Silva: Reductions between certain incidenceproblems and the Continuum Hypothesis
Barcelona Set Theory Seminar
3/15/2019
BCNSETS
BARCELONA RESEARCH GROUP IN SET THEORY
BARCELONA SET THEORY SEMINAR
Reductions between certain incidence
problems and the Continuum Hypothesis
Samuel Gomes da Silva
UFBA, Brazil
Abstract: We consider two families of incidence problems, C 1 and C 2 ,
which are related to real numbers and countable subsets of the real
line. Instances of problems in C 1 are as follows: given a real number x,
pick randomly a countable set A of reals hoping that x is in A, whereas
instances of problems in C 2 are as follows: given a countable set A of
reals, pick randomly a real number x hoping that x is not in A. One could
arguably defend that, at least intuitively, problems in C 2 are easier to
solve than problems in C 1 . Indeed, we show that, after some suitable
formalization, one can prove (in ZFC) that, on the one hand, problems in
C 2 are at least as simple to solve as problems in C 1 . On the other hand,
the statement ``Problems in C 1 have the exact same complexity as
problems in C 2 '' is equivalent to the Continuum Hypothesis.
Date: Thursday 21 March 2019
Time: 16:00
Place: Room S-1*
Departament de Matemàtiques i Informàtica
Universitat de Barcelona
Gran Via de les Corts Catalanes 585, 08007 Barcelona
* Enter the University building through the door 20 meters to the right of the main
door and, as you enter the courtyard, turn left, go to the end of the corridor, and
then downstairs.
Tagged: Samuel Gomes da Silva
Jonathan Verner: Towers in filters, cardinal invariants, and Luzin type families, part II
Prague Set Theory Seminar
3/14/2019
Dear all,
The seminar meets on Wednesday March 20th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Jonathan Verner will continue his talk from the last seminar:
Towers in filters, cardinal invariants, and Luzin type families
Jonathan will present results from his recent paper (with J. Brendle, B.
Farkas);
We investigate which filters on ω can contain towers, that is, a modulo
finite descending sequence without any pseudointersection. We prove the
following results:
(1) Many classical examples of nice tall filters contain no towers.
(2) It is consistent that tall analytic P-filters contain towers of
arbitrary regular height.
(3) It is consistent that all towers generate non-meager filters.
(4) The statement “Every ultrafilter contains towers.” is independent of
ZFC.
Best,
David
Tagged: Jonathan Verner
Francisco Guevara Parra: Analytic spaces and their Tukey types
Toronto Set Theory Seminar
3/12/2019
Place: Fields Institute (Room 210)
Date: March 15, 2018 (13:30-15:00)
Speaker: Francisco Guevara Parra
Title: Analytic spaces and their Tukey types
Abstract: In this Thesis we study topologies on countable sets from the
perspective of Tukey reductions of their neighbourhood
filters. In particular we will study $k$-analytic group topologies
on $\omega$. This will allow us to obtain a metrization theorem
for analytic sequential group topologies on $\omega$, as well
as a classification of such groups in terms of the Tukey type of
the filter of neighbourhoods of the identity. Recall that
a countable topological space is analytic if the topology is analytic
as a subset of the Cantor space.
Tagged: Francisco Guevara Parra
Christopher Lambie-Hanson: Chromatic numbers of finite subgraphs
Kurt Godel Research Center
3/11/2019
Talk held by Christopher Lambie-Hanson (Virginia Commonwealth University, Richmond, USA) at the KGRC seminar on 2019-03-14.
Abstract: By the De Bruijn-Erdős Compactness Theorem, if a graph $G$ has infinite chromatic number, then it has finite subgraphs of arbitrarily large finite chromatic number. We can therefore define an increasing function $f_G:\omega\to \omega$ by letting $f_G(n)$ be the least number of vertices in a subgraph of $G$ with chromatic number $n$. We will show in ZFC that, for every function $f:\omega\to \omega$ there is a graph $G$ with chromatic number $\aleph_1$ such that $f_G$ grows faster than $f$. This answers a question of Erdős, Hajnal, and Szemeredi. Time permitting, we will discuss connections between our proof and various diamond and club-guessing principles.
Miguel Moreno: The Main Gap in the generalized Borel-reducibility hierarchy
Israeli Logic Talks
3/10/2019
BIU Infinite Combinatorics Seminar
Mon, 11/03/2019 - 13:00
Speaker: Miguel Moreno (BIU)
Title: The Main Gap in the generalized Borel-reducibility hierarchy
Abstract. During this talk we will discuss where in the generalized Borel-reducibility hierarchy are the isomorphism relation of first order complete theories. These theories are divided in two kind:classifiable and non-classifiable. To study the classifiable theories case is needed the use of Ehrenfeucht-Fraïssé games. On the other hand the study of the non-classifiable theories is done by using colored trees. The goal of the talk is to see the classifiable theories case and start the non-classifiable theories case by proving that it is possible to map every element of the generalized Baire, f, into a colored tree, J(f), such that; for every f and g elements of the generalized Baire space, J(f) and J(g) are isomorphic as colored trees if and only if f and g coincide on a club.
Tagged: Miguel Moreno
Boise Extravaganza in Set Theory (BEST) 2019 Conference, June 19-21
Conference
3/8/2019
We are pleased to announce that the 2019 Boise Extravaganza in Set Theory will take place in Ashland, Oregon, on the campus of Southern Oregon University, during June 19-21.
BEST is an international conference featuring talks on a broad range of recent advances in set theory research. It particularly aims to support the careers of young researchers in set theory. The conference is organized by the Set Theory group at Boise State University and is structured as a symposium of the 100th annual meeting of the American Association for the Advancement of Science, Pacific Division (AAAS-PD).
Travel grants will be available for students and postdocs participating in the conference.
Please visit the BEST web site, which will be updated with more details as they become available.
Organizers Liljana Babinkostova (Boise State University), John Clemens (Boise State University), Samuel Coskey (Boise State University), Marion Scheepers (Boise State University)
Scientific Committee Natasha Dobrinen (University of Denver), Simon Thomas (Rutgers University)
July 29-31, 2019, Zukunftskolleg, University of Konstanz, Germany
2nd instalment of the Forcing Project Networking Conferences seriesWebsite: https://fpnc2019.forcing-project.com
Organization: Carolin Antos, Neil Barton, Deborah Kant, Daniel Kuby (University of Konstanz)
Invited Speakers
Joan Bagaria (University of Barcelona)
Mirna Džamonja (University of East Anglia)
Leon Horsten (University of Bristol)
Juliette Kennedy (University of Helsinki)
Godehard Link (MCMP, Munich)
Marianna Antonutti Marfori (MCMP, Munich)
Toby Meadows (University of California, Irvine)
Call for Papers
The project “Forcing: Conceptual Change in the Foundations of Mathematics” (2018-2023) aims to analyse the development of modern set theory since the introduction of the forcing technique both from a historical and philosophical point of view. It brings together methods and research questions from different research areas in the history and philosophy of mathematics to investigate if and how the extensive use of the forcing method brought about a conceptual change in set theory; and in which ways this may influence the philosophy of set theory and the foundations of mathematics.
The research group organises a series of Networking Conferences with the goal of reaching out to researchers from these different areas. The second instalment will be devoted to the topic of recent set theory as a bridge between mathematics and philosophy and focuses on the interaction between mathematical and philosophical arguments and views in set theory. Set theory has long been both a mathematical discipline and a program with foundational motivations. It seems that this dual character makes it a natural crossway between mathematics and philosophy, possibly more so than other mathematical disciplines.
Topics
We welcome contributions which
a) add to current discussions in the philosophy of set theory (set-theoretic pluralism, height and width potentialism/actualism, the universe/multiverse debate, the forcing technique, justification of new axioms, contrasts with other foundational frameworks) by relating philosophical and mathematical arguments to one another; by working out the philosophical import of set-theoretic results; or by giving set-theoretic explications of philosophical concepts;
b) question or uphold the relevance of philosophical arguments in set theory. For example, according to Penelope Maddy's naturalism, first philosophical arguments play no justificatory role in set theory. Should (mathematical) naturalism be understood in Maddy's style? Are there other forms of naturalism that are more tolerant of traditional philosophical questions?
c) analyse the mathematical and philosophical content of the concept "set-theoretic practice" as used in recent set-theoretic programs. For example, do the different foundational programmes offered by the likes of Friedman, Hamkins and Woodin constitute different set-theoretic practices?d) investigate how the inclusion of alternative set theories (constructive set theory, class theories, set theories based on non-classical logic, categorial theories of sets) impact the philosophy of set theory.
Submissions
Abstracts of 300-500 words should be submitted in PDF (with LaTeX source) or Word format no later than March 31, 2019, via email to <submissions@forcing-project.com>. Notifications of acceptance will be issued by April 15, 2019.
Financial support
As we would like to enable early career researchers (including PhD students) to apply, we are in the process of organizing funding for travel and accommodation for the contributed speakers. Please contact the organizers for further information.
Conference registration
The conference is free (no conference fee) and everyone is welcome to attend. For logistical reasons, please register by sending an email to <registration@forcing-project.com> before July 1, 2019.
Tagged: Godehard Link, Joan Bagaria, Juliette Kennedy, Leon Horsten, Marianna Antonutti Marfori, Mirna Džamonja, Toby Meadows
Jonathan Verner: Towers in filters, cardinal invariants, and Luzin type families
Prague Set Theory Seminar
3/7/2019
Dear all,
The seminar meets on Wednesday March 13th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Jonathan Verner -- Towers in filters, cardinal invariants, and
Luzin type families
Jonathan will present results from his recent paper (with J. Brendle, B.
Farkas);
We investigate which filters on ω can contain towers, that is, a modulo
finite descending sequence without any pseudointersection. We prove the
following results:
(1) Many classical examples of nice tall filters contain no towers.
(2) It is consistent that tall analytic P-filters contain towers of
arbitrary regular height.
(3) It is consistent that all towers generate non-meager filters.
(4) The statement “Every ultrafilter contains towers.” is independent of
ZFC.
Best,
David
Tagged: Jonathan Verner
Wong Tin Lok: End extensions and subsystems of second-order arithmetic
NUS Logic Seminar
3/7/2019
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 13 March 2019, 17:00 hrs
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Wong Tin Lok
Title: End extensions and subsystems of second-order arithmetic
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
Investigations in reverse mathematics reveal that most naturally
occurring theorems in mathematics are equivalent to one of five
arithmetic axioms nowadays known as the BIG FIVE. These provide
strong empirical evidence for the importance of the Big Five.
In the talk, I will attempt to explain their importance mathematically
in terms of the characteristics of their models.
The work to be presented is joint with Stephen G. Simpson (Vanderbilt).
Tagged: Wong Tin Lok
Serhii Bardyla - Complete topological semigroups
Kurt Godel Research Center
3/6/2019
Talk held by Serhii Bardyla (KGRC) at the KGRC seminar on 2019-03-07.
Abstract: The first part of the talk will be devoted to the investigation of completeness in the class of topological semigroups.
Then we shall discuss a topologization of semigroups of partial isomorphisms between principal ideals of a tree.
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 6 March 2019, 17:00 hrs
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Dilip Raghavan
Title: A small ultrafilter number
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: It is proved to be consistent relative to a measurable
cardinal that there is a uniform ultrafilter on the real numbers which
is generated by fewer than the maximum possible number of sets. It is
also shown to be consistent relative to a supercompact cardinal that
there is a uniform ultrafilter on aleph_{omega+1} which is generated
by fewer than 2^{aleph_{omega+1}} sets.
This is joint work with Saharon Shelah.
Tagged: Dilip Raghavan
Yann Pequignot: Finite versus infinite: an insufficient shift
Toronto Set Theory Seminar
3/5/2019
Place: Fields Institute (Room 210)
Date: , 2018 (13:30-15:00)
Speaker: Yann Pequignot
Title: Finite versus infinite: an insufficient shift
Abstract: The Borel chromatic number – introduced by Kechris, Solecki, and Todorcevic (1999) – generalizes the chromatic number to Borel graphs. While the G_0 dichotomy states that there exists a minimal graph with uncountable Borel chromatic number, it turns out that characterizing when a graph has infinite Borel chromatic number is far more intricate. Even in the case of graphs generated by a single function, the situation is quite complicated. The Shift Graph on the space of infinite subsets of natural numbers is generated by the function that removes the minimum element. It is acyclic but has infinite Borel chromatic number. In 1999, Kechris, Solecki, and Todorcevic asked whether the Shift Graph is minimal among the graphs generated by a single Borel function that have infinite Borel chromatic number. I will sketch a proof that the answer is negative using descriptive complexity considerations and a representation theorem for Sigma^1_2 sets due to Marcone (1994). This result has recently been considerably strengthened by Todorcevic and Vidnyanszky who proved that the set of closed subsets of the Shift Graph that have infinite Borel Chromatic number is Pi^1_2 complete, therefore ruling out most interesting basis results for this class of Borel graphs.
Tagged: Yann Pequignot
Hector Alonzo Barriga-Acosta: Some combinatorics on the normality of the countable box product of the convergent sequence
Carnegie Mellon Logic Seminar
3/1/2019
Mathematical logic seminar - Mar 5 2019
Time: 3:30pm - 4:30 pm
Room: Wean Hall 8220
Speaker: Hector Alonzo Barriga Acosta
Universidad Nacional Autónoma de México
Title: Some combinatorics on the normality of the countable box product
of the convergent sequence
Abstract:
The normality of □ (ω + 1)^ω is a question raised in the 40's (it is
known
that consistently this space is normal). Through the years many different
tecniques have been developed, but non of them have solved the question in
ZFC. We'll take a look to a combinatorial point of view, given by Judy
Roitman, of this problem.
Tagged: Hector Alonzo Barriga-Acosta
Michal Doucha: Definable pseudometrics and Borel reductions between them
Prague Set Theory Seminar
3/1/2019
Dear all,
The seminar meets on Wednesday March 6th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Michal Doucha -- Definable pseudometrics and Borel reductions
between them
I will introduce a ``continuous generalizatio'' of the theory of
definable equivalence relations and Borel reductions between them.
Equivalence relations will be replaced by pseudometrics and reductions
between them will be replaced by certain uniformly continuous maps. I
will explain our motivation and prove some basic results. I will present
some open problems whose solutions may require completely new ideas from
invariant descriptive set theory. It will be based on a joint paper with
Marek Cúth and Ondřej Kurka.
Tagged: Michal Doucha
Alejandro Poveda: Prikry-type forcing and the failure of the Singular Cardinal Hypothesis
Barcelona Set Theory Seminar
2/28/2019
BCNSETS
BARCELONA RESEARCH GROUP IN SET THEORY
BARCELONA SET THEORY SEMINAR
Prikry-type forcing and the failure of the
Singular Cardinal Hypothesis
Alejandro Poveda
Universitat de Barcelona
Abstract: Prikry-type forcing plays a central role in
combinatorics due to its close links with central set-theoretic
principles such as the Singular Cardinal Hypothesis (SCH) or the
Tree Property. The original Prikry forcing was devised to change
the cofinality of a measurable cardinal to ω, but there are now
many other more sophisticated constructions that yield more
powerful applications. Among them we can find Magidor and
Radin forcing for changing cofinalities to uncountable cardinals.
In this session we will describe the Prikry forcing with collapses
and present a proof of Magidor’s theorem on the consistency,
relative to appropriate large cardinal hypotheses, of the failure
of the SCH at the first singular cardinal.
Date: Thursday 7 March 2019
Time: 16:00
Place: Room S-1*
Departament de Matemàtiques i Informàtica
Universitat de Barcelona
Gran Via de les Corts Catalanes 585, 08007 Barcelona
* Enter the University building through the door 20 meters to the right of the
main door and, as you enter the courtyard, turn left, go to the end of the
corridor, and then downstairs.
Tagged: Alejandro Poveda
Sandra Müller: Projective determinacy for games of length $\omega^2$ and longer
We will study infinite two player games and the large cardinal strength corresponding to their determinacy. For games of length $\omega$ this is well understood and there is a tight connection between the determinacy of projective games and the existence of canonical inner models with Woodin cardinals. For games of arbitrary countable length, Itay Neeman proved the determinacy of analytic games of length $\omega \cdot \theta$ for countable $\theta\> \omega$ from a sharp for $\theta$ Woodin cardinals.
We aim for a converse at successor ordinals. In joint work with Juan P. Aguilera we showed that determinacy of $\boldsymbol\Pi^1\_{n+1}$ games of length $\omega^2$ implies the existence of a premouse with $\omega+n$ Woodin cardinals. This generalizes to a premouse with $\omega+\omega$ Woodin cardinals from the determinacy of games of length $\omega^2$ with $\Game^{\mathbb{R}}\boldsymbol\Pi^1\_1$ payoff.
If time allows, we will also sketch how these methods can be adapted to, in combination with results of Nam Trang, obtain $\omega^\alpha+n$ Woodin cardinals for countable ordinals $\alpha$ and natural numbers $n$ from the determinacy of sufficiently long projective games.
Mathematical logic seminar - Feb 26 2019
Time: 3:30pm - 4:30 pm
Room: Wean Hall 8220
Speaker: Raphaël Carroy (KGRC, Vienna)
Title: Strongly surjective linear orders
Abstract:
When a linear order has an increasing surjection onto each of its
suborders we say that it is strongly surjective. We prove that countable
strongly surjective orders are the union of an analytic and a coanalytic
set, and that moreover they are complete for this class of sets. If time
allows it, I'll also discuss the existence of uncountable strongly
surjective orders. This is a joint work with Riccardo Camerlo and Alberto
Marcone.
Tagged: Raphaël Carroy
Jan Grebík: Vizing's Theorem for Graphings
Prague Set Theory Seminar
2/22/2019
Dear all,
The seminar meets on Wednesday February 27th at 11:00 in the Institute
of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Jan Grebík -- Vizing's Theorem for Graphings
I will show that the measurable edge chromatic index of a graphing G
(bounded degree Borel graph with invariant measure) with maximum degree
D is D+1. This is a joint work with Oleg Pikhurko.
Best,
David
Tagged: Jan Grebík
Barnabas Farkas: Degrees of destruction
Wrocław University of Technology
2/22/2019
Tuesday, February 26, 2019, 17:15
Wrocław University of Technology, 215 D-1
Speaker: Barnabas Farkas (TU Wien)
Title: Degrees of destruction
Abstract:
I'm going to present a survey on our results (joint with L. Zdomskyy) about the following strong notion of destroying Borel ideals: We say that the forcing notion $\mathbb{P}$ $+$-destroys the Borel ideal $\mathcal{I}$ if $\mathbb{P}$ adds an $\mathcal{I}$-positive $\dot{X}$ which has finite intersection with every $A\in \mathcal{I}\cap V$. I will
talk about the following:
(1) Examples when usual destruction (that is, when $\dot{X}$ required to be infinite only) implies $+$-destruction, and when it does not.
(2) Characterization of those Borel ideals which can be $+$-destroyed, in particular, we will see that if $\mathcal{I}$ can be $+$-destroyed then the associated Mathias-Prikry forcing $+$-destroys it.
(3) Characterization of those analytic P-ideals which are $+$-destroyed by the associated Laver-Prikry forcing.
Tagged: Barnabas Farkas
Alejandro Poveda: Prikry-type forcing: properties and applications
Barcelona Set Theory Seminar
2/20/2019
BCNSETS
BARCELONA RESEARCH GROUP IN SET THEORY
BARCELONA SET THEORY SEMINAR
Prikry-type forcing: properties and applications
Alejandro Poveda
Universitat de Barcelona
Abstract: Prikry-type forcing plays a central role in
combinatorics due to its close links with central set-theoretic
principles such as the Singular Cardinal Hypothesis (SCH) or the
Tree Property. The original Prikry forcing was devised to change
the cofinality of a measurable cardinal to ω, but there are now
many other more sophisticated constructions that yield more
powerful applications. Among them we can find Magidor and
Radin forcing for changing cofinalities to uncountable cardinals,
or the Diagonal supercompact Prikry forcing with collapses, due
also to Magidor, which can be used to force the failure of SCH
at the first singular cardinal. In this session we will prove some
of the key properties of Prikry forcing and will see how it is
used to prove the consistency of the negation of SCH.
Date: Thursday 28 February 2019
Time: 16:00
Place: Room S-1*
Departament de Matemàtiques i Informàtica
Universitat de Barcelona
Gran Via de les Corts Catalanes 585, 08007 Barcelona
* Enter the University building through the door 20 meters to the right of the
main door and, as you enter the courtyard, turn left, go to the end of the
corridor, and then downstairs.
Tagged: Alejandro Poveda
Registration open for the Advanced Class and ESTC2019
Conference
2/18/2019
We opened registration for both the European Set Theory Conference and the Advanced Class (YST2019). You can register to the events separately by following the links below.
European Set Theory Conference 2019:
Early bird registration: Until the 15th of April. Fee: 150 Euro.
Late registration: Until the 31st of May. Fee: 200 Euro.
Early bird registration: Until the 15th of April. Fee: 150 Euro.
Late registration: Until the 31st of May. Fee: 200 Euro.
Please note the instructions for transferring the registration fee, in particular, the distinct Payment Reference numbers for the two conferences.
We are looking forward to seeing you in Vienna!
Assaf Shani: Borel reducibility and symmetric models
Carnegie Mellon Logic Seminar
2/17/2019
Mathematical logic seminar - Feb 19 2019
Time: 3:30pm - 4:30 pm
Room: Wean Hall 8220
Speaker: Assaf Shani
Department of Mathematics
UCLA
Title: Borel reducibility and symmetric models
Mathematical logic seminar - Feb 19 2019
Time: 3:30pm - 4:30 pm
Room: Wean Hall 8220
Speaker: Assaf Shani
Department of Mathematics
UCLA
Title: Borel reducibility and symmetric models
Abstract:
We develop a correspondence between the study of Borel equivalence relations induced by closed subgroups of S∞, and the study of symmetric models of set theory without choice, and apply it to prove a conjecture of Hjorth-Kechris-Louveau (1998). For example, we show that the equivalence relation ≅*ω+1,0 is strictly below ≅*ω+1 in Borel reducibility. By results of Hjorth-Kechris-Louveau, ≅*ω+1 corresponds to Σ0ω+1 actions of S∞, while ≅*ω+1,0 corresponds to Σ0ω+1 actions of "well behaved" closed subgroups of S∞, for example abelian groups. For these proofs we analyze the models Mn, n<ω, developed by Monro (1973), and extend his construction past ω, through all countable ordinals. This answers a question of Karagila (2016).
Tagged: Assaf Shani
Liu Yong: There is no strong minimal pair
NUS Logic Seminar
2/15/2019
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 20 February 2019, 17:00 hrs
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Liu Yong.
Title: There is no strong minimal pair.
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
A strong minimal pair in r.e. degrees is defined to be a pair of
A, B such that they are incomparable and for any non-recursive r.e. set W
below A, B+W computes A. Historically, this was a difficult problem.
Slaman showed a weaker version of this (i.e. B+W computes a third set C,
instead of A), and it is called Slaman-Triple nowadays. Only recently,
people showed that there is a strong minimal pair. However, we realized
that there is a problem in that paper. Then we turned the problem into a
proof that there is no strong minimal pair. In this talk, we will sketch
the proof.
Tagged: Liu Yong
Asaf Karagila: Staring into a Cohen real: the Bristol model
Prague Set Theory Seminar
2/14/2019
The seminar meets on Wednesday February 20th at 11:00 in the Institute
of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Asaf Karagila -- Staring into a Cohen real: the Bristol model
What kind of intermediate models can be found when adding a Cohen real,
c, to L? If we are concerned with models of ZFC, then answer is simple:
L itself, or Cohen extensions of L.
But when models of ZF are of interest, this fails spectacularly. The
Bristol model is a model intermediate to L[c] which is not even
constructible from a set. We will discuss the details of the
construction, and the consequences it has on the models which are
trapped between L and L[c].
Tagged: Asaf Karagila
Dominik Adolf: The strength of very small Jonsson cardinals
An uncountable cardinal κ is Jonnson if only if the set of proper subsets of κ that are of cardinality κ is stationary. Though this property has large cardinal strength it is not at all clear that Jonnson cardinals do in fact need to be large in the obvious sense. For example, it is known that Jonsson cardinals can be singular.
In this talk we will use the methods of Inner Model Theory to show that, given the assumption that the least singular cardinal is Jonsson, there is a canonical model with a strong cardinal together with a class of Silver indiscernibles for this model. (The proof presented will make some simplifying assumptions.) Time permitting, we may discuss approaches to extend this result to show the existence of inner models with Woodin cardinals and more.
Tagged: Dominik Adolf
David Schrittesser: The Ramsey property, MAD families, and their multidimensional relatives
Toronto Set Theory Seminar
2/14/2019
Place: Fields Institute (Room 210)
Date: February 15, 2018 (13:30-15:00)
Speaker: David Schrittesser
Title: The Ramsey property, MAD families, and their multidimensional relatives
Abstract: Suppose every set of real numbers has the Ramsey property and “uniformization on Ellentuck-comeager sets” as well as Dependent Choice hold (as is the case under the Axiom of Determinacy, but also in Solovay’s model). Then there are no MAD families. As it turns out, there are also no (Fin x Fin)-MAD families, where Fin x Fin is the two-dimensional Fubini product of the ideal of finite sets. We also comment on higher dimensional products. Results are joint work with Asger Törnquist.
Tagged: David Schrittesser
Set-theoretic methods in topology and real functions theory, Kosice, September 9-13, 2019
Conference
2/13/2019
Set-theoretic methods in topology and real functions theory,
dedicated to 80th birthday of Lev Bukovsky
September 9-13, 2019
The conference takes place in Kosice, the city located in eastern Slovakia. There is a nice occasion of celebrating 80th birthday of Lev Bukovsky this year, who spent most of his life in the city. The webpage of the meeting is
Topics of interest include set-theoretic topology, descriptive set theory, cardinal invariants, selection principles and set-theoretic aspects of the convergence of functions.
The program consists of lectures provided by invited speakers:
Aleksander Blaszczyk
Vera Fischer
Istvan Juhasz
Menachem Magidor
Dilip Raghavan
Boaz Tsaban
and contributed talks of participants.
Participants registration with welcome reception starts on Sunday evening, September 8. The online registration at the webpage of the meeting is open from March till June 30. Due to Visegrad Fund we may partially support the accommodation of small number of PhD students or young researchers, from Visegrad Countries, Eastern Partnership Countries or Western Balkans Countries.
Tagged: Aleksander Blaszczyk, Boaz Tsaban, Dilip Raghavan, István Juhász, Menachem Magidor, Vera Fischer
Jan Hubička: Combinatorial proofs of the extension property for partial automorphisms
Prague Set Theory Seminar
2/11/2019
Dear all,
The seminar meets on Wednesday February 13th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Jan Hubička -- Combinatorial proofs of the extension property for partial automorphisms
Class K of finite structures has extension property for partial automorphisms (EPPA) if for every A in K there exists B in K such that every partial automorphism of A (that is isomorphism of two substructures of A) extends to automorphism of B. Hrushovski, in 1992,
shown that the class of all finite graphs has EPPA. This result was used by Hodges, Hodkinson, Lascar and Shelah to show that the random
graph has small index property. This motivated search for new classes with EPPA. I will show (and partly prove) new general theorem giving a structural condition for class having EPPA. The theorem is a strengthening of the Herwig--Lascar theorem, but the proof techniques are new, combinatorial and completely self-contained.
I will also discuss connection to structural Ramsey theory.
This is joint work with Jaroslav Nesetril and Matej Konecny.
Best,
David
Matthias Baaz: On the benefit of unsound rules: Henkin quantifiers and beyond
NUS Logic Seminar
2/9/2019
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 13 February 2019, 17:00 hrs
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Matthias Baaz
Title: On the benefit of unsound rules: Henkin quantifiers and beyond
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
We give examples of analytic sequent calculi LK+ and LK++ that
extend Gentzen's sequent calculus LK by unsound quantifier rules
in such a way that (i) derivations lead only to true sequents
(ii) cut free proofs may be non-elementary shorter than cut free LK proofs.
This research is based on properties of Hilbert's epsilon calculus and
is part of efforts to complement Hilber's stepwise concept of proof by
useful global concepts.
We use these ideas to provide analytic calculi for Henkin quantifiers and
demonstrate soundness, (cut free) completeness and cut elimination.
Furthermore, we show, that in the case of quantifier macros such as Henkin
quantifiers for a partial semantics global calculi are the only option to
preserve analyticity.
Tagged: Matthias Baaz
Daniel T. Soukup: Uniformization properties and graph edge colourings
Sierpinski's now classical result states that there is an edge 2-colouring of the complete graph on aleph1 vertices so that there are no uncountable monochromatic subgraphs. In the 1970s, Erdos, Galvin and Hajnal asked what other graphs with large chromatic number admit similar edge colourings i.e., with no 'large' monochromatic subgraphs. We plan to review some recent advances on this problem and in particular, connect the question to Shelah's ladder system uniformization theory.
Tagged: Daniel Soukup
Clinton Conley: Ode on a one-ended subforest
Carnegie Mellon Logic Seminar
2/8/2019
Mathematical logic seminar - Feb 12 2019
Time: 3:30pm - 4:30 pm
Room: Wean Hall 8220
Speaker: Clinton Conley
Department of Mathematical Sciences
CMU
Title: Ode on a one-ended subforest
Abstract:
Many arguments in (finite) graph theory follow this pattern: postpone some
onerous task until the last possible moment, after you've arranged things
to make the task as easy as possible. In the descriptive set-theoretic
milieu, the one-ended forest provides a portal to a procrastinator's
wonderland in which the onerous task instead wanders off to infinity. We
discuss a few instances of this phenomenon and some applications to
coloring and treeing graphs.
Tagged: Clinton Conley
Alejandro Poveda: An invitation to the world of Prikry-type forcing
Barcelona Set Theory Seminar
2/8/2019
BCNSETS
BARCELONA RESEARCH GROUP IN SET THEORY
BARCELONA SET THEORY SEMINAR
An invitation to the world of Prikry-type forcing
Alejandro Poveda
Universitat de Barcelona
Abstract: Prikry-type forcing plays a central role in
combinatorics due to its close links with central set-theoretic
principles such as the Singular Cardinal Hypothesis (SCH) or the
Tree Property. The original Prikry forcing was devised to change
the cofinality of a measurable cardinal to ω, but there are now
many other more sophisticated constructions that yield more
powerful applications. Among them we can find Magidor and
Radin forcing for changing cofinalities to uncountable cardinals,
or the Diagonal supercompact Prikry forcing with collapses, due
also to Magidor, which can be used to force the failure of SCH
at the first singular cardinal. In this session we will give an
introduction from the very beginning to this family of forcings,
and if time permits we will present some easy applications.
Date: Thursday 14 February 2019
Time: 16:00
Place: Room S-1*
Departament de Matemàtiques i Informàtica
Universitat de Barcelona
Gran Via de les Corts Catalanes 585, 08007 Barcelona
* Enter the University building through the door 20 meters to the right of the
main door and, as you enter the courtyard, turn left, go to the end of the
corridor, and then downstairs.
Tagged: Alejandro Poveda
Damjan Kalajdzievski: How to show Con(ZFC + omega_1=u<a) from Con(ZFC)
Toronto Set Theory Seminar
2/7/2019
Place: Fields Institute (Room 210)
Date: February 8 , 2019 (13:30-15:00)
Speaker: Damjan Kalajdzievski
Title: How to show Con(ZFC + omega_1=u<a) from Con(ZFC)
Abstract: I will outline how to prove the result in the title by joint work with Osvaldo Guzman
Tagged: Damjan Kalajdzievski
James Cummings: More on compactness
Carnegie Mellon Logic Seminar
2/4/2019
Mathematical logic seminar - Feb 5 2019
Time: 3:30pm - 4:30 pm
Room: Wean Hall 8220
Speaker: James Cummings
Department of Mathematical Sciences
CMU
Title: More on compactness
Abstract:
I'll discuss compactness phenomena at regular cardinals, particularly successors of singular cardinals. In particular I'll explain why ℵω+1 is in some respects completely different from ℵω2+1.
(This talk is related to the talks about compactness that I gave in the Fall semester, but is logically independent)
Tagged: James Cummings
Sandra Müller: The consistency strength of long projective determinacy
Bristol Logic Seminar
2/4/2019
Tuesday, February 5, 2019, 15.00
Howard House 4th Floor Seminar Room, University of Bristol
Speaker: Sandra Müller (University of Vienna)
Title: The consistency strength of long projective determinacy
Abstract:
We will study infinite two player games and the large cardinal strength corresponding to their determinacy. For games of length $\omega$ this is well understood and there is a tight connection between the determinacy of projective games and the existence of canonical inner models with Woodin cardinals. For games of arbitrary countable length, Itay Neeman proved the determinacy of analytic games of length $\omega \cdot \theta$ for countable $\theta> \omega$ from a sharp for $\theta$ Woodin cardinals.
We aim for a converse at successor ordinals. In joint work with Juan P. Aguilera we showed that determinacy of $\boldsymbol\Pi^1_{n+1}$ games of length $\omega^2$ implies the existence of a premouse with $\omega+n$ Woodin cardinals. This generalizes to a premouse with $\omega+\omega$ Woodin cardinals from the determinacy of games of length $\omega^2$ with $\Game^{\mathbb{R}}\boldsymbol\Pi^1_1$ payoff.
If time allows, we will also sketch how these methods can be adapted to, in combination with results of Nam Trang, obtain $\omega^\alpha+n$ Woodin cardinals for countable ordinals $\alpha$ and natural numbers $n$ from the determinacy of sufficiently long projective games.
Bristol Logic Seminars: https://www.bristolmathsresearch.org/events/logic-and-set-theory/
Tagged: Sandra Müller
Alessandro Vignati: Uniform Roe coronas
IMPAN Working Group in Applications of Set Theory
2/4/2019
Seminar: Working group in applications of set theory, IMPAN
(joint meeting with the Geometric Group Theory Seminar, IMPAN)
Thursday, 7.02.2019, 10:15, room 403, IMPAN
NOTE ROOM CHANGE TO 403
Speaker: Alessandro Vignati (KU Leuven)
Title: "Uniform Roe coronas"
Abstact: "Given a metric space (X,d), one defines a subalgebra of the space of operators on l_2(X) called the uniform Roe algebra of (X,d), denoted C_u*(X). This is the closure of the algebra of finite-propagation operators. The study of these algebras comes from the fact that C_u*(X) catches algebraically some of the large scale geometrical properties of X. Uniform Roe algebras have therefore an intrinsic relation with coarse geometry and the coarse Baum-Connes conjecture.
In recent year, much work was dedicated to show which geometric properties are preserved by isomorphisms of Uniform Roe algebras. Namely, if C_u*(X) and C_u*(Y) are isomorphic, how much do X and Y look alike? We pose the same question for Uniform Roe corona algebras.
Since Cu*(X) contains all compact operators, we can define the natural quotient Q_u*(X)=C_u*(X)/K(l_2(X)), the Uniform Roe corona algebra of X. Which geometric properties do the spaces X and Y share, when an isomorphism between Q_u*(X) and Q_u*(Y) is given? For example, must X and Y be coarsely equivalent, or even bijectively coarsely equivalent? (Two spaces are coarsely equivalent if "they look the same when the observer is far from them").
We answer these questions with the aid of some set theory, in particular of Forcing Axioms. Forcing Axioms are generalizations of the Baire category theorem. They are alternative to the Continuum Hypothesis, and they're at the base of many rigidity phenomena observed in the theory of quotients (both discrete such as Boolean algebra quotient, and continuous, as the Calkin algebra or corona C*-algebras). The talk starts with introducing the objects in play. The goal is to state the main results, and at least sketch the salient points of their proofs. We conclude with a list of open questions. This is joint work with Bruno Braga and Ilijas Farah".
This is the last meeting during the first semester of 2018/19.
Visit our seminar page which may include information on some future talks at https://www.impan.pl/~set_theory/Seminar/
Tagged: Alessandro Vignati
Moritz Müller: Forcing against bounded arithmetic
Barcelona Set Theory Seminar
2/1/2019
BARCELONA RESEARCH GROUP IN SET THEORY
BARCELONA SET THEORY SEMINAR
Forcing against bounded arithmetic
Moritz Müller
Universitat Politècnica de Catalunya
Abstract: We study the following problem. Given a nonstandard
model of arithmetic we want to expand it by a binary relation that
does something prohibitive, e.g. violates the pigeonhole principle in
the sense that it is the graph of a bijection from n+1 onto n for
some (nonstandard) n in the model. The goal is to do so while
preserving as much as possible of true arithmetic. More precisely,
we want the expansion to model the least number principle for a
class of formulas as large as possible. The problem is of central
importance in bounded arithmetic and propositional proof
complexity. It is not well understood. The talk describes a general
method of forcing to produce such expansions.
Date: Thursday 7 February 2019
Time: 16:00
Place: Room S-1*
Departament de Matemàtiques i Informàtica
Universitat de Barcelona
Gran Via de les Corts Catalanes 585, 08007 Barcelona
* Enter the University building through the door 20 meters to the right of the
main door and, as you enter the courtyard, turn left, go to the end of the
corridor, and then downstairs.
Tagged: Moritz Müller
Piotr Szewczak: Selection Principles in Mathematics (an overview)
Israeli Logic Talks
2/1/2019
BIU Infinite Combinatorics Seminar
Piotr Szewczak, Cardinal Stefan Wyszyński University in Warsaw, Poland
The theory of selection principles deals with the possibility of obtaining mathematically significant objects by selecting elements from sequences of sets. The studied properties mainly include covering properties, measure- and category-theoretic properties, and local properties in topological spaces, especially functions spaces. Often, the characterization of a mathematical property using a selection principle is a nontrivial task leading to new insights on the characterized property.
I will give an overview of this theory and, if time permits, I will present some results obtained jointly with Boaz Tsaban and Lyubomyr Zdomskyy.
Tagged: Piotr Szewczak
Berkeley conference on inner model theory, July 08--19, 2019
Logic Fest in the Windy City, Chicago, May 30 - June 2, 2019
Conference
1/31/2019
The conference will take place at the University of Illinois at Chicago on May 30 - June 2. We will cover topics in set theory, descriptive set theory, model theory, and various applications. The workshop is aimed at graduate students and postdocs, but can also be beneficial to anyone interested in current developments in logic. We will have three tutorials and several talks. The invited speakers are:
Tutorials:
Travel support is available. Requests should be directed to Dima Sinapova. Graduate students, young researchers, female mathematicians and members of underrepresented groups are particularly encouraged to apply. Schedule of talks.
Lodging:
Tagged: Anton Bernshteyn, Artem Chernikov, Filippo Calderoni, John Krueger, Maryanthe Malliaris, Natasha Dobrinen, Sherwood Hachtman, Spencer Unger, Will Boney
Jordi Lopez Abad: Amalgamation and Ramsey properties of $\ell_p^n$'s
Prague Set Theory Seminar
1/29/2019
The seminar meets again on Wednesday February 6th at 11:00 in the
Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front
building.
Program: Jordi Lopez Abad -- Amalgamation and Ramsey properties of
$\ell_p^n$'s
We will give a proof of the fact that $\{\ell_p^n\}$ have the
approximate Ramsey property and a strong form of amalgamation (they are
Fraïssé classes, in a metric sense). The proofs are divided into 3
cases: $p=\infty$, $p=2$ and $p\neq 2,\infty$. We will also discuss the
case of the families of all finite dimensional subspaces of $L_p(0,1)$
for $p\neq 2,\infty$ and of $C[0,1]$.
Tagged: Jordi Lopez-Abad
Feng Qi: On investigation of some foundational problems of economics
NUS Logic Seminar
1/29/2019
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 30 January 2019, 17:00 hrs
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Feng Qi
Title: On investigation of some foundational problems of economics
Abstract: I shall present some of my toughts regarding some foundational
problems of economics from mathematical logic point of view.
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Tagged: Qi Feng
Arturo Martínez-Celis: Porous sets on the Cantor set
IMPAN Working Group in Applications of Set Theory
1/27/2019
Seminar: Working group in applications of set theory, IMPAN
Thursday, 31.01.2019, 10:15, room 105, IMPAN
Speaker: Arturo Martínez-Celis (IM PAN)
Title: "Porous sets on the Cantor set"
Abstact: "Given a completely metrizable space X, a subset A of X is a strongly porous set if there is a positive constant p such that for any open ball B of radius r smaller than 1, there is an open ball B' inside of B of radius rp such that B' evades the set A. We will study the cardinal invariants related to the σ-ideal generated by strongly porous sets on the Cantor space and its relation with other known σ-ideals of the real line. We will also uncover a deep connection between the σ-ideal of the strongly porous sets and some instances of the Martin's Axiom. ".
Visit our seminar page which may include information on some future talks at https://www.impan.pl/~set_theory/Seminar/
Tagged: Arturo Antonio Martinez
Anton Bernshteyn: Independent Sets in Algebraic Hypergraphs
Carnegie Mellon Logic Seminar
1/26/2019
Mathematical logic seminar - Jan 29 2019
Time: 3:30pm - 4:30 pm
Room: Wean Hall 8220
Speaker: Anton Bernshteyn
Department of Mathematical Sciences
CMU
Title: Independent Sets in Algebraic Hypergraphs
Abstract:
An active avenue of research in modern combinatorics is extending classical extremal results to the so-called sparse random setting. The basic hope is that certain properties that a given "dense" structure is known to enjoy should be inherited by a randomly chosen "sparse" substructure. One of the powerful general approaches for proving such results is the hypergraph containers method, developed independently by Balogh, Morris, and Samotij and Saxton and Thomason. Another major line of study is establishing combinatorial results for algebraic or, more generally, definable structures. In this talk, we will combine the two directions and address the following problem: Given a "dense" algebraically defined hypergraph, when can we show that the subhypergraph induced by a generic low-dimensional algebraic set of vertices is also fairly "dense"? This is joint work with Michelle Delcourt (University of Waterloo) and Anush Tserunyan (University of Illinois at Urbana--Champaign).
Tagged: Anton Bernshteyn
John Truss: Surjectively rigid chains
Bristol Logic Seminar
1/25/2019
Tuesday, January 29, 2019, 15.00
Howard House 4th Floor Seminar Room, University of Bristol
Speaker: John Truss (University of Leeds )
Title: Surjectively rigid chains
Abstract:
A classical result of Dushnik and Miller establishes the existence of a dense subchain of the ordered set of real numbers, which has no automorphisms, apart from the identity. In joint work with Manfred Droste, we showed that such rigid chains can be constructed which nevertheless admit many non-trivial embeddings (order-isomorphisms to subsets), and constructions are also given of any uncountable regular cardinality which are rigid for automorphisms, but which admit many non-trivial embeddings; in this case, stationary sets are used to encode a dense set of p[pints in the order constructed. In joint work with Mayra Montalvo-Ballesteros, these results are extended to consider also epimorphisms (order-preserving surjections) and in some cases, general endomorphisms.
Bristol Logic Seminars: https://www.bristolmathsresearch.org/events/logic-and-set-theory/
Tagged: John Truss
Joan Bagaria: The consistency strength of simultaneous stationary reflection
Barcelona Set Theory Seminar
1/23/2019
BCNSETS
BARCELONA RESEARCH GROUP IN SET THEORY
BARCELONA SET THEORY SEMINAR
ICREA and Universitat de Barcelona
The consistency strength of simultaneous
stationary reflection
Joan Bagaria
ICREA and Universitat de Barcelona
Abstract: We shall present M. Magidor’s beautiful proof that if a
regular cardinal k reflects simultaneously all pairs of its stationary
subsets, then k is a weakly compact cardinal in the constructible
universe L. We will then discuss some of the difficulties involved in
extending Magidor’s result to the hyperstationary case.
Date: Thursday 31 January 2019
Time: 15:30
Place: Room S-1
Departament de Matemàtiques i Informàtica
Universitat de Barcelona
Gran Via de les Corts Catalanes 585
08007 Barcelona
* Enter the University building through the door 20 meters to the right of the
main door and, as you enter the courtyard, turn left, go to the end of the
corridor, and go downstairs.
Tagged: Andrew Arana, Andrew Brooke-Taylor, Åsa Hirvonen, Asaf Karagila, Assaf Rinot, Auli Salmi, Colin McLarty, David Aspero, David Schrittesser, Dima Sinapova, Filippo Calderoni, Hugh Woodin, John Baldwin, John Steel, Joni Puljujärvi, Jouko Väänänen, Juan Pablo Aguilera, Juliette Kennedy, Marcin Sabok, Maria-Clara Cortes, Menachem Magidor, Michael Hrusak, Miguel Angel Mota, Miguel Moreno, Natasha Dobrinen, Otto Rajala, Rodrigo Jesus Hernandez Gutierrez, Sandra Müller, Tapio Saarinen, Ulises Ariet Ramos Garcia, Vera Fischer, Vincenzo Dimonte, Xianghui Shi, Yurii Khomskii
Benjamin Vejnar: Complexity of the homeomorphism relation between compact spaces
Kurt Godel Research Center
1/21/2019
Talk held by Benjamin Vejnar (Charles University, Prague, Czech Republic) at the KGRC seminar on 2019-01-24.
Abstract: We study the complexity of the homeomorphism relation of compact metrizable spaces when restricted to some subclasses such as continua, regular continua or regular compacta. The complexity of an equivalence relation on a Polish space is compared with some others (e.g. with the universal orbit equivalence relation) using the notion of Borel reducibility.
Sakae Fuchino: Reflection Principles formulated as Löwenheim-Skolem Theorems for stationary logics and the Continuum Problem
Bristol Logic Seminar
1/18/2019
Tuesday, January 22, 2019, 15.00
Howard House 4th Floor Seminar Room, University of Bristol
Speaker: Sakae Fuchino (Kobe University )
Title: Reflection Principles formulated as Löwenheim-Skolem Theorems for stationary logics and the Continuum Problem
Abstract:
We give characterizations of variations of Löwenheim-Skolem Theorem for stationary logic (i.e. the logic with monadic second order variables which run over countable subsets of a structure and with the quantifier "there exist stationarily many countable sets such that ..."). Löwenheim-Skolem Theorems with reflection cardinal $<\aleph_2$ for this logic and some variants of it are shown to be equivalent either to the Diagonal Reflection Principle (DRP) down to internally club sets introduced by Sean Cox or this type of DRP plus CH.
The Löwenheim-Skolem Theorem for stationary logics with reflection cardinal "$<2^{\aleph_0}$" is not consistent with very large continuum. However, Löwenheim-Skolem Theorem for this logics with reflection cardinal "$<2^{\aleph_0}$" in terms of an internal interpretation of the stationary logic is consistent with the continuum being very large. The Löwenheim-Skolem Theorem for stationary logics with reflection cardinal "$<2^{\aleph_0}$" in terms of stationary logic with an internal ${\mathcal P}_{\kappa}{\lambda}$-interpretation of second order variables even implies that the continuum is (at least) weakly Mahlo.
The results presented in this talk are going to be included in a joint paper with André Ottembreit and Hiroshi Sakai.
Seminar link: https://www.bristolmathsresearch.org/events/logic-and-set-theory/
Keita Yokoyama: Ekeland's variational principle in reverse mathematics
NUS Logic Seminar
1/17/2019
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 23 January 2018, 17:00 hrs
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Keita Yokoyama
Title: Ekeland's variational principle in reverse mathematics
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: Ekeland's variational principle is a key theorem used in various
areas of analysis such as continuous optimization, fixed point theory and
functional analysis. It guarantees the existence of pseudo minimal
solutions of optimization problems on complete metric spaces. Let f be
a positive real valued continuous (or lower semi-continuous) function
on a complete metric space (X,d). Then, a point x in X is said to be a
pseudo minimum if f(x)=f(y)+d(x,y) implies x=y. Now, Ekeland's
variational principle says that for any point a in X, there exists a
pseudo minimum x such that f(x)<=f(a)-d(a,x). In reverse
mathematics, it is observed that many theorems for continuous
optimization problems are provable within the system of arithmetical
comprehension (ACA-0), and thus most such problems have arithmetical
solutions. However, this is not the case for pseudo minima. We will
see that Ekeland's variational principle or its restriction to the
space of continuous functions C([0,1]) are both equivalent to
Pi-1-1-comprehenstion. This is a joint work with Paul Shafer and David
Fernandez-Duque.
Logic Seminar 23 Jan 2019 17:00 hrs at NUS
NUS Logic Seminar
1/17/2019
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 23 January 2018, 17:00 hrs
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Keita Yokoyama
Title: Ekeland's variational principle in reverse mathematics
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: Ekeland's variational principle is a key theorem used in various
areas of analysis such as continuous optimization, fixed point theory and
functional analysis. It guarantees the existence of pseudo minimal
solutions of optimization problems on complete metric spaces. Let f be
a positive real valued continuous (or lower semi-continuous) function
on a complete metric space (X,d). Then, a point x in X is said to be a
pseudo minimum if f(x)=f(y)+d(x,y) implies x=y. Now, Ekeland's
variational principle says that for any point a in X, there exists a
pseudo minimum x such that f(x)<=f(a)-d(a,x). In reverse
mathematics, it is observed that many theorems for continuous
optimization problems are provable within the system of arithmetical
comprehension (ACA-0), and thus most such problems have arithmetical
solutions. However, this is not the case for pseudo minima. We will
see that Ekeland's variational principle or its restriction to the
space of continuous functions C([0,1]) are both equivalent to
Pi-1-1-comprehenstion. This is a joint work with Paul Shafer and David
Fernandez-Duque.
Kaethe Minden: Split Principles and Splitting Families
Prague Set Theory Seminar
1/16/2019
Dear all,
The seminar meets on Wednesday January 23rd at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Kaethe Minden -- Split Principles and Splitting Families
The original split principle is an equivalent formulation of a cardinal
failing to satisfy the combinatorial essence of weak compactness. The
notion was then expanded by Gunter Fuchs and me to characterize the
negation of other large cardinal properties. Split principles give rise
to seemingly new large cardinals, and some new ideals, for example a
normal ideal on $\mathcal P_\kappa \lambda$ in the case of
$\lambda$-Shelahness. In this talk I introduce split principles and
connect them to certain new notions of splitting numbers being large.
Best,
David
Tagged: Kaethe Minden
Marcin Sabok: Measurable Hall's theorem for actions of Z^n
Toronto Set Theory Seminar
1/16/2019
Place: Fields Institute (Room 210)
Date: January 18, 2018 (13:30-15:00)
Speaker: Marcin Sabok
Title: Measurable Hall's theorem for actions of Z^n
Abstract: In the 1920's Tarski asked if it is possible to divide the unit square into finitely many pieces, rearrange them by translations and get a disc of area 1. It turns out that this is possible and proved by Laczkovich in the 1990's. His decomposition, however, used non-measurable pieces and seemed paradoxical. Recently, Grabowski, Mathe and Pikhurko and Marks and Unger showed that such decompositions can be obtained using nice measurable pieces. During the talk, I will discuss a measurable version of the Hall marriage theorem for actions of finitely generated abelian groups. This result implies that for measurable actions of such groups, if two equidistributed measurable sets are equidecomposable, then they are equidecomposalble using measurable pieces. The latter generalizes the measurable circle squaring result by Grabowski, Mathe and Pikhurko. This is joint work with Tomasz Ciesla.
Tagged: Marcin Sabok
Moritz Müller: Forcing against bounded arithmetic
Kurt Godel Research Center
1/15/2019
Talk held by Moritz Müller (Universitat Politècnica de Catalunya, Barcelona, Spain) at the KGRC seminar on 2019-01-17.
Abstract: We study the following problem. Given a nonstandard model of arithmetic we
want to expand it by a binary relation that does something prohibitive,
e.g. violates the pigeonhole principle in the sense that it is the graph
of a bijection from $n+1$ onto $n$ for some (nonstandard) $n$ in the
model. The goal is to do so while preserving as much as possible of true
arithmetic. More precisely, we want the expansion to model the least
number principle for a class of formulas as large as possible. The problem
is of central importance in bounded arithmetic and propositional proof
complexity. It is not well understood. The talk describes a general method
of forcing to produce such expansions.
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 16 January 2018, 17:00 hrs
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Frank Stephan
Title: Lampligher groups and automata
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Joint work with:
Sanjay Jain, Birzhan Moldagaliyev and Tien Dat Tran.
Abstract:
This talk is about representing lamplighter groups using
computational models from automata theory. It will be shown that
if G can be presented such that the full group operation
is recognised by a transducer, then the same is true for the lampgligher
group of G created by taking the restricted wreath product of
G with the group of integers Z. Furthermore, Cayley presentations,
where only multiplications with constants are recognised by transducers,
are used to study generalised lampglighter groups where one
takes the restricted wreath product of G over a d-dimensional
copy of the integers or the free group with d generators.
Additionally, if G is a finite group then the restricted wreath
product of G over the two-dimensional group of integers is Cayley
tree automatic.
The paper is available at
http://www.comp.nus.edu.sg/~fstephan/transducergroup.ps
Tagged: Frank Stephan
Tomasz Weiss: Accessible points, harmonic measure and the Riemann mapping
IMPAN Working Group in Applications of Set Theory
1/14/2019
Seminar: Working group in applications of set theory, IMPAN
Thursday, 17.01.2019, 10:15, room 105, IMPAN
Speaker: Tomasz Weiss (UKSW)
Title: "Accessible points, harmonic measure and the Riemann mapping"
Abstact: "Let D be a bounded domain in R_n, n larger than 1. We provide an elementary proof that the set of all boundary accessible points of D is an analytic set. We investigate the nature of the set of accessible points of D when n=2 using only set theoretical methods. We provide also a view of the relation between harmonic measure in D, if n=2, D simply connected, and the Riemann mapping of D. In this talk we prove new results and give easier proofs of known results".
Visit our seminar page which may include information on some future talks at https://www.impan.pl/~set_theory/Seminar/
Tagged: Tomasz Weiss
Menachem Magidor: Omitting types in the logic of metric structures
Israeli Logic Talks
1/13/2019
HUJI Logic Seminar
16/Jan/2019, 11-13, Ross 63.
Speaker: Menachem Magidor
Title: Omitting types in the logic of metric structures
Abstract.
(joint work with I. Farah)
The logic of metric structures was introduced by Ben Yaacov, Berenstein , Henson and Usvyatsov. It is a version of continuous logic which allows fruitful model theory for many kinds of metric structures. There are many aspects of this logic which make it similar to first order logic, like compactness, a complete proof system, an omitting types theorem for complete types etc. But when one tries to generalize the omitting type criteria to general (non-complete) types the problem turns out to be essentially more difficult than the first order situation. For instance one can have two types (in a complete theory) that each one can be omitted, but they can not be omitted simultaneously.
In the beginning of the talk we shall give a brief survey of the logic of metric structures, so the talk should be accessible also the listeners who are not familiar with the logic of metric structures.
Tagged: Menachem Magidor
Miha Habic: The ultrapower capturing property (part II)
Prague Set Theory Seminar
1/10/2019
Dear all,
The seminar meets on Wednesday January 16th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Miha Habic -- The ultrapower capturing property (part II)
In 1993 Cummings showed that it is consistent (relative to large
cardinals) that there is a measurable cardinal kappa carrying a normal
measure whose ultrapower contains the whole powerset of kappa^+. He
showed that nontrivial large cardinal strength was necessary for this,
but it was not clear whether this capturing property had any direct
consequences. Recently Radek Honzík and I showed that it is relatively
consistent that the least measurable cardinal has this capturing
property. We also considered a local version of capturing. In this talk
I will introduce a forcing notion due to Apter and Shelah and the
modifications necessary to obtain our result.
Best,
David
Tagged: Miha Habic
Arno Pauly: Uniformity aspects of determinacy
Bristol Logic Seminar
1/7/2019
Tuesday, January 8, 2019, 15.00
Howard House 4th Floor Seminar Room, University of Bristol
Speaker: Arno Pauly (Swansea University)
Title: Uniformity aspects of determinacy
Abstract:
We consider uniformity aspects of determinacy for some low-level point-classes. The formal framework for this is Weihrauch reducibility, which will be introduced. We distinguish two cases: For games on Cantor space with winning sets from the Hausdorff difference hierarchy, we find that there is a player such that the knowledge that she will win does not help the task of a constructing a winning strategy. This does not hold for open winning sets on Baire space -- here knowing who wins the game makes it easier to construct a winning strategy. Open determinacy on Baire space shares all known properties with the perfect tree theorem (a closed subset of Baire space is either countable or contains a perfect subset), but it is an open question whether they are actually equivalent.
The results presented are from joint work with Takayuki Kihara and Alberto Marcone (https://arxiv.org/abs/1812.01549) and with Stephane Le Roux (https://arxiv.org/abs/1407.5587).
Tagged: Arno Pauly
Daria Michlik: Symmetric products as cones
Wrocław University of Technology
1/7/2019
Tuesday, January 8, 2019, 17:15
Wrocław University of Technology, 215 D-1
Speaker: Daria Michlik (Cardinal Stefan Wyszynski University in Warsaw)
Title: Symmetric products as cones
Abstract:
(join work with Alejandro Illanes and Veronica Martinez-de-la-Vega)
For a continuum $X$, let $F_n(X)$ be the hyperspace of all nonempty subsets of $X$ with at most $n$-points. The space $F_n(X)$ is called the n'th-symmetric product.
In
A. Illanes, V. Martinez-de-la-Vega, Symmetric products as cones, Topology Appl. 228 (2017), 36–46
it was proved that if $X$ is a cone, then its hyperspace $F_n(X)$ is also a cone.
During my talk I will discuss the converse problem. I will prove that if $X$ is a locally connected curve, then the following conditions are equivalent:
1. $X$ is a cone,
2. $F_n(X)$ is a cone for some $n\ge 2$,
3. $F_n(X)$ is a cone for each $n\ge 2$.
Tagged: Daria Michlik
Tomasz Kochanek: Rosenthal's lemma and its applications
IMPAN Working Group in Applications of Set Theory
1/7/2019
Seminar: Working group in applications of set theory, IMPAN
Thursday, 10.01.2019, 10:15, room 105, IMPAN
Speaker: Tomasz Kochanek (IMPAN/UW)
Title: "Rosenthal's lemma and its applications "
Abstact: "In this instructional talk we will recall Rosenthal's lemma on uniformly bounded sequences of measures and present its several classical applications in the Banach space and vector measures theory. First, we will prove the surprising Nikodym's uniform boundedness principle and Phillips' lemma where the application of Rosenthal's result makes the proofs much easier than the original ones. A few further corollaries of Nikodym's principle will be mentioned, such as the Dieudonné-Grothendieck theorem on bounded vector measures and the Seever theorem on the range of an operator into a B(Σ)-space. Next, we shall prove two beautiful consequences of Rosenthal's lemma: the Diestel-Faires theorem and the Orlicz-Pettis theorem. If time allows, we will also briefly discuss their further deep consequences in the structural theory of Banach spaces".
Visit our seminar page which may include information on some future talks at https://www.impan.pl/~set_theory/Seminar/
Tagged: Tomasz Kochanek
Natasha Dobrinen: Mini-course on Infinitary Ramsey theory
Kurt Godel Research Center
1/7/2019
Time and Place: Tuesday, January 8 and Wednesday, January 9 at 10:30am in the KGRC lecture room (both parts) at the KGRC.
Part I. Topological Ramsey spaces and applications to ultrafilters Part II. Ramsey theory on trees and applications to big Ramsey degrees
The Infinite Ramsey Theorem states that given $n,r\ge 1$ and a coloring of
all $n$-sized subsets of $\mathbb{N}$ into $r$ colors, there is an
infinite subset of $\mathbb{N}$ in which all $n$-sized subsets have the
same color. There are several natural ways of extending Ramsey's Theorem.
One extension is to color infinite sets rather than finite sets. In this
case, the Axiom of Choice precludes a full-fledged generalization, but
upon restricting to definable colorings, much can still be said. Another
way to extend Ramsey's Theorem is to color finite sub-objects of an
infinite structure, requiring an infinite substructure isomorphic to the
original one. While it is not possible in general to obtain substructures
on which the coloring is monochromatic, sometimes one can find bounds on
the number of colors, and this can have implications in topological
dynamics.
In Part I, we will trace the development of Ramsey theory on the Baire
space, from the Nash-Williams Theorem for colorings of clopen sets to the
Galvin-Prikry Theorem for Borel colorings, culminating in Ellentuck's
Theorem correlating the Ramsey property with the property of Baire in a
topology refining the metric topology on the Baire space. This refinement
is called the Ellentuck topology and is closely connected with Mathias
forcing. Several classical spaces with similar properties will be
presented, including the Carlson-Simpson space and the Milliken space of
block sequences. From these we shall derive the key properties of
topological Ramsey spaces, first abstracted by Carlson and Simpson and
more recently given a refined presentation by Todorcevic in his book {\em
Introduction to Ramsey spaces}. As the Mathias forcing is closely
connected with Ramsey ultrafilters, via forcing mod finite initial
segments, so too any Ramsey space has a $\sigma$-closed version which
forces an ultrafilter with partition properties. Part I will show how
Ramsey spaces can be used to find general schemata into which disparate
results on ultrafilters can be seen as special cases, as well as obtain
fine-tuned results for structures involving ultrafilters.
Part II will focus on Ramsey theory on trees and their applications to
Ramsey theory of homogeneous structures. An infinite structure is {\em
homogeneous} if each isomorphism between two finite substructures can be
extended to an automorphism of the infinite structure. The rationals as a
linearly ordered structure and the Rado graph are prime examples of
homogeneous structures. Given a coloring of singletons in the rationals,
one can find a subset isomorphic to the rationals in which all singletons
have the same color. However, when one colors pairs of rationals, there
is a coloring due to Sierpinski for which any subset isomorphic to the
rationals has more than one color on its pairsets. This is the origin of
the theory of {\em big Ramsey degrees}, a term coined by Kechris, Pestov
and Todorcevic, which investigates bounds on colorings of finite
structures inside infinite structures. Somewhat surprisingly, a theorem
of Halpern and L\"{a}uchli involves colorings of products of trees,
discovered en route to a proof that the Boolean Prime Ideal Theorem is
strictly weaker than the Axiom of Choice, is the heart of most results on
big Ramsey degrees. We will survey big Ramsey degree results on countable
and uncountable structures and related Ramsey theorems on trees, including
various results of Dobrinen, Devlin, D\v{z}amonja, Hathaway, Larson,
Laver, Mitchell, Shelah, and Zhang.
Natasha Dobrinen: Ramsey Theory of the Henson graphs
Kurt Godel Research Center
1/7/2019
Abstract: A central question in the theory of ultrahomogeneous relational structures asks, How close of an analogue to the Infinite Ramsey Theorem does it carry? An infinite structure S is ultrahomogeneous if any isomorphism between two finitely generated substructures of S can be extended to an automorphism of S. We say that S has finite big Ramsey degrees if for each finite substructure A of S, there is a number n(A) such that any coloring of the copies of A in S can be reduced to no more than n(A) colors on some substructure S′ of S, which is isomorphic to the original S.
The two main obstacles to a fuller development of this area have been lack of representations and general Milliken-style theorems. We will present new work proving that the Henson graphs, the kk-clique free analogues of the Rado graph for k≥3, have finite big Ramsey degrees. We devise representations of Henson graphs via strong coding trees and prove Milliken-style theorems for these trees. Central to the proof is the method of forcing, building on Harrington's proof of the Halpern-Läuchli Theorem.
Miha Habic: The ultrapower capturing property (part I)
Prague Set Theory Seminar
1/1/2019
The seminar meets on Wednesday January 9th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Miha Habic -- The ultrapower capturing property (part I)
In 1993 Cummings showed that it is consistent (relative to large
cardinals) that there is a measurable cardinal kappa carrying a normal
measure whose ultrapower contains the whole powerset of kappa^+. He
showed that nontrivial large cardinal strength was necessary for this,
but it was not clear whether this capturing property had any direct
consequences. Recently Radek Honzík and I showed that it is relatively
consistent that the least measurable cardinal has this capturing
property. We also considered a local version of capturing. In this talk
I will overview the necessary large cardinal machinery and Cummings'
original argument.
The second part of the talk will take place on Wednesday January 16th.
In the second talk Miha will introduce a forcing notion due to Apter and
Shelah and the modifications necessary to obtain the result.